This document should give you an idea on how the internet evolved into what we know now, it should serve as a time line for important events, only the most important, there are thousands and thousands of other events not mentioned here, what is mentioned here is the really important events.
1957 USSR launches Sputnik, ARPA and DoD plan for a technology advance.
1962 USA looking for a way to control nuclear missiles after a strike
1968 ARPNET, The mother internet was found between four nodes, first internet.
1972 First Email program and Email protocol
1973 TCP/IP started with an idea of a protocol
1974 INTERNET, term first coined
1976 The coaxial cable set grounds for LAN
1979 USENET was born
1981 National Science Foundation introduces CSNET at 56Kbs, A separate network
1983 ARPANET adopts TCP only
1984 ARPANET was divided into two networks: MILNET and ARPANET
1986 The Internet Engineering Task Force or IETF was created
1987 BITNET and CSNET merged to form the Corporation for Research and Educational Networking (CREN)
1990 Merit, IBM and MCI formed a not for profit corporation called ANS, Advanced Network & Services
1991 CSNET (which consisted of 56Kbps lines) was discontinued having fulfilled its important early role in the provision of academic networking service.
1992 Internet Society is chartered, World-Wide Web released by CERN, NSFNET backbone upgraded to T3 (44.736Mbps)
   

It all started in 1957 when the former USSR launches Sputnik, the first manufactured earth satellite (the earths only natural satellite is the moon). In response, the United States forms the Advanced Research Projects Agency (ARPA) within the Department of Defense (DoD) to establish US lead in science and technology applicable to the military, it was nothing like what you see today, at this stage FTP was years away, there were no hosts yet, no backbone either, Just a plan.

In 1962 RAND Paul Baran, of the RAND Corporation (a government agency), was commissioned by the U.S. Air Force to do a study on how it could maintain its command and control over its missiles and bombers, after a nuclear attack. This was to be a military research network that could survive a nuclear strike, decentralized so that if any locations (cities) in the U.S. were attacked, the military could still have control of nuclear arms for a counter-attack., Baran's finished document described several ways to accomplish this. His final proposal was a packet switched network. Packet switching that is still used today (in most computer networks) is the breaking down of data into datagrams or "packets" that are labeled to indicate the origin and the destination of the information and the forwarding of these packets from one computer to another computer until the information arrives at its final destination computer. This was crucial to the realization of a computer network. If packets are lost at any given point, the message can be resent by the originator." Still the internet was not really alive, no hosts, no Backbone,

In 1968 ARPNET of BBN was born, Honeywell minicomputer was the switch, a year later in 1969 four nodes were established, University of California at Los Angeles, SRI (in Stanford), University of California at Santa Barbara, and University of Utah. The network was wired together via 50 Kbps (The first ever backbone) circuits, and the four nodes are our 4 HOSTS !, so there you go, even though only 4 hosts, the internet is officially alive under a different name.

In 1972 Ray Tomlinson of BBN created the Email protocol along with an Email program (the original program does not run on today's computers), In that same year, ARPA was renames to DARPA short for Defense Advanced Research Projects Agency, ARPANET was at the time using the Network Control Protocol or NCP to transfer data. This allowed communications between hosts running on the same network, By this time, though the backbone was still at 50Kbps (a bit slower than your dialup modem), there were 23 hosts up and running, including the initial four,

You may want to skip this part if you are in a hurry
Quoted from RedHat Network (http://www.redhat.com/docs/manuals/linux/RHL-8.0-Manual/ref-guide/s1-email-sendmail.html)
 

History

Sendmail's roots can be traced to the birth of email, occurring in the decade before the birth of ARPANET, the precursor to the Internet. In those days, every user's mailbox was a file that only they had rights to read, and mail applications simply added text to that file. Every user had to wade through their mail file to find any old mail, and reading new mail was a equally difficult. The first actual transfer of a mail message file from one host to another did not take place until 1972, when email began to be moved by FTP over the NCP network protocol. This easier method of communication quickly became popular, even to the point where it made up most of ARPANET's traffic in less than a year.

However, a lack of standardization between competing protocols made email much harder to send from some systems. This continued until the ARPANET standardized on TCP/IP in 1982. Soon after, a new protocol, SMTP, materialized for transporting email messages. These developments, combined with HOSTS files being replaced with DNS, allowed full-featured MTAs to materialize. Sendmail, which grew out of an earlier email delivery system called Delivermail, quickly became the standard as the email began to expand and become widely used.

In 1973 TCP/IP was about to be created (although the name came later) by a group headed by Vinton Cerf from Stanford and Bob Kahn from DARPA. This new protocol was to allow diverse computer networks to interconnect and communicate with each other, We still use an enhanced version of that protocol,

In 1974 the term internet was first coined by Vint Cerf and Bob Kahn in paper on TCP (Transmission Control Protocol).

Two years later in 1976 the LAN was being evolved with the development of the coaxial cable, by this time, there were over 110 hosts and ARPANET was still running at 50Kbps (like it started), but with the great addition of satellite and radio,

In 1979 USENET (Yes the same news network you probably know) was created by Steve Bellovin, a graduate student at University of North Carolina, and programmers Tom Truscott and Jim Ellis. It was based on UUCP, The Creation of BITNET, by IBM, "Because its Time Network", introduced the "store and forward" network. It was used for email and listservs, Now it looks like you can see how the internet was coming up,

In 1981 a separate network *(CSNET) was introduced by the National Science Foundation, running at 56Kbps, Vinton Cerf proposed a plan for an inter-network connection between CSNET and the ARPANET. By this time hosts on both networks were well above 200 !

Two years later in 1983 Internet Activities Board (IAB) was created, On January 1st if that same year, every machine connected to ARPANET had to use TCP/IP. TCP/IP became the core Internet protocol and replaced NCP entirely. in addition and on that same year, The University of Wisconsin created Domain Name System (DNS). This allowed packets to be directed to a domain name, which would be translated by the server database into the corresponding IP number. This made it much easier for people to access other servers, because they no longer had to remember numbers. In this year there were more than 550 hosts up and running

in 1984 ARPANET was divided into two networks: MILNET and ARPANET. MILNET was to serve the needs of the military and ARPANET to support the advanced research component, Department of Defense continued to support both networks. was divided into two networks: MILNET and ARPANET. MILNET was to serve the needs of the military and ARPANET to support the advanced research component, Department of Defense continued to support both networks.

Upgrade to CSNET was contracted to MCI. New circuits would be T1 lines,1.5 Mbps which is twenty-five times faster than the old 56 Kbps lines. IBM would provide advanced routers and Merit would manage the network. New network was to be called NSFNET (National Science Foundation Network), and old lines were to remain called CSNET.

Even though there were more than one thousand hosts by this time, ARPANET and CSNET did not change, it was until 1985 that T1 came into the picture when The National Science Foundation started installing them on NSFNET.

in 1986 The Internet Engineering Task Force or IETF was created to serve as a forum for technical coordination by contractors for DARPA working on ARPANET, US Defense Data Network (DDN), and the Internet core gateway system.

In 1987 BITNET and CSNET merged to form the Corporation for Research and Educational Networking (CREN), another work of the National Science Foundation.

The National Science Foundation Finished installing T1 on NSFNET lines in 1988, Where the need for faster lines was the motive for starting the upgrade again !

In 1990 Merit, IBM and MCI formed a not for profit corporation called ANS, Advanced Network & Services, which was to conduct research into high speed networking. It soon came up with the concept of the T3, a 45 Mbps line. NSF quickly adopted the new network and by the end of 1991 all of its sites were connected by this new backbone.

While the T3 lines were being constructed, the Department of Defense replaced ARPANET with the NSFNET backbone. The original 50Kbs lines of ARPANET were taken out of service.

Tim Berners-Lee (Now works for CNN if i recall correctly) and CERN in Geneva implements a hypertext system to provide efficient information access to the members of the international high-energy physics community.

1991 CSNET (which consisted of 56Kbps lines) was discontinued having fulfilled its important early role in the provision of academic networking service. A key feature of CREN is that its operational costs are fully met through dues paid by its member organizations.

The NSF established a new network, named NREN, the National Research and Education Network. The purpose of this network is to conduct high speed networking research. It was not to be used as a commercial network, nor was it to be used tosend a lot of the data that the Internet now transfers.

A year later in 1992 Internet Society is chartered, World-Wide Web released by CERN, NSFNET backbone upgraded to T3 (44.736Mbps)

At this stage, the backbones were NSFNET at 45Mbps (T3) , private interconnected backbones of 56Kbps, 1.544Mbps, satellite and radio connections - Number of hosts was approximately 1,136,000,

in 1993 InterNIC created by NSF to provide specific Internet services: directory and database services (by AT&T), registration services (by Network Solutions Inc.), and information services (by General Atomics/CERFnet). Marc Andreessen and NCSA and the University of Illinois develops a graphical user interface to the WWW, called "Mosaic for X", X is the UNIX user interface above the shell, Mosaic became the netscape navigator you probably know ! Mosaic was also released for windows. in January, 1997 the mosaic project was abandoned. if you like a copy of mosaic that runs under windows can be downloaded here, You should note that this version will run on windows 95, for other versions, you will have to try and see.

Backbones: 45Mbps (T3) NSFNET, private interconnected backbones consisting mainly of 56Kbps, 1.544Mbps, and 45Mpbs lines, plus satellite and radio connections - Hosts: 2,056,000

1994 No major changes were made to the physical network. The most significant thing that happened was the growth. Many new networks were added to the NSF backbone. Hundreds of thousands of new hosts were added to the INTERNET during this time period, The internet was really accessible to the public and businesses started using it, Pizza Hut offers pizza ordering on its Web page for example, First Virtual, the first cyberbank, opens. ATM (Asynchronous Transmission Mode, 145Mbps) backbone is installed on NSFNET.

Backbones: 145Mbps (ATM) NSFNET, private interconnected backbones consisting mainly of 56Kbps, 1.544Mbps, and 45Mpbs lines, plus satellite and radio connections - Hosts: 3,864,000

in 1995 The National Science Foundation announced that as of April 30, 1995 it would no longer allow direct access to the NSF backbone. The National Science Foundation contracted with four companies that would be providers of access to the NSF backbone (Merit). These companies would then sell connections to groups, organizations, and companies.

a $50 annual fee is imposed on domains, excluding .edu and .gov domains which are still funded by the National Science Foundation.

Backbones: 145Mbps (ATM) NSFNET (now private), private interconnected backbones consisting mainly of 56Kbps, 1.544Mbps, 45Mpbs, 155Mpbs lines in construction, plus satellite and radio connections - Hosts: 6,642,000

1996-now

Most Internet traffic is carried by backbones of independent ISPs, including MCI, AT&T, Sprint, UUnet, BBN planet, ANS, and many many others..

The new problem now is the problem of IP addresses, as you know the demand is enormous and the ip range is (although very big) not enough, the new challenge would be a new range without going down with the internet, a challenge of running a new TCP system and keeping the current system functional

Backbones:
145Mbps (ATM) NSFNET (now private)
private interconnected backbones consisting mainly of 56Kbps, 1.544Mbps, 45Mpbs, and 155Mpbs lines, plus satellite and radio connections - Hosts: over 15,000,000, and growing rapidly