"I think there is a world market for maybe five computers"
Thomas J. Watson (CEO of IBM), 1943
Roots
I guess since humans have fingers, they started to count and compute with them, and since they have tools, they started to carve numbers into bones.
Across different cultures and timelines there have been different kinds of numbering systems to compute with.
Our global civilization uses mostly the Hindu-Arabic-Numbers with the decimal number system, based on 10, our computers use commonly the binary number system, based on 2, the famous 0s and 1s. But there have been other cultures with other systems, the Maya with an base 20, Babylon with base 60, or the Chinese with base 16, the hexadecimal system, which is also used in computer science.
The first compute devices were mechanical helpers, like the Abacus, Napier's Bones or Slide Rule, they did not perform computations on their own, but were used to represent numbers and apply arithmetic operations on them like addition, subtraction, multiplication and division.
Mechanical Computers
The first mechanical computing machine is considered to be the Antikythera Mechanism, found in an Greek ship that sunk about 70 BC. But actually it is no computer, cos it does not perform computations, but an analog, astrological clock, a sun and moon calendar that shows solar and lunar eclipses.
In the 17th century first mechanical computing machines were proposed and build.
Wilhelm Schickard designed a not fully functional prototype in 1623.
The Pascaline, designed by Blaise Pascal in 1642, was the first operational and commercial available mechanical computer, able to perform the 4 basic arithmetic operations.
In 1672 the German mathematician Gottfried Wilhelm Leibniz invented the stepped cylinder, used in his not fully functional Stepped Reckoner.
With the Curta the use of mechanical calculators lived on, up to the advent of portable electronic calculators in the 1960s.
Programmable Computers
The punch card for programming a machine was introduced by Joseph Marie Jacquard in 1804 with his automated weaving loom, the Jacquard Loom, for producing textiles with complex patterns.
In 1837 Charles Babbage (considered as the father of the computer) was the first to describe a programmable, mechanical computer, the Analytical Engine.
Ada Lovelace (considered as the mother of programming) worked with Babbage and was the first person to publish a computer algorithm, the computation of Bernoulli numbers.
Babbage was his time ahead, as he described all parts, CPU, memory, input/output, a modern computer has, but was not able to realize his machine due to missing funds and proper engineering abilities of that time.
About a century later, Konrad Zuse's Z3, built in 1941, is considered to be the first binary, free programmable computer.
It used 600 telephone relays for computation and 1400 relays for memory, a keyboard and punched tape as input, lamps as output, and it operated with 5 Hertz.
Mainframes
Zuse's machines mark the advent of the first mainframes used by military and science during and after WWII.
Colossus Mark I (1943), ENIAC (1945), IBM 704 (1954) for example used vacuum tubes instead of relays and were replaced more and more by transistor based computers in the 1960s.
Home Computers
With small chips, integrated circuits, it was possible to build smaller and reasonable Home Computers in the 1970s. IBM and other big players underestimated this market, so Atari, Apple, Commodore, Sinclair, etc. started the Home Computer Revolution, one computer for every home.
Some first versions came as self-assembly kit, like the Altair 8800 (1975), or with built in TV output, like the Apple I (1976), or as fully assembled video game console like the Atari VCS (1977), followed by more performant versions with an graphical user interface, like the Apple Mac (1984), or the Commodore Amiga 1000 (1985).
Personal Computers
IBM started in 1981 with the 5150 the Personal Computer era. Third party developers were able to provide operating systems, like Microsoft DOS, or hardware extensions for the standardized extension slots, like hard-drives, video-cards, sound-cards, etc., soon other companies created clones of the IBM PC, the famous "PC Compatible".
Gaming was already in the Home Computer era an important sales argument, the early PC graphics standards like CGA and EGA were not really able to compete with the graphics generated by the Denise chip in an Commodore Amiga 500, but with the rise of SVGA (1989) standards and the compute power of the Intel 486 CPU (1989), game forges were able to build games with superior 3D graphics, like Wolfenstein 3D (1992), Comanche (1992) or Strike Commander (1993) and the race for higher display resolutions and more detailed 3D graphics continues until today.
With operating systems based on graphical user interfaces, like OS/2, X11, Windows 95 in the 1990s, PCs finally replaced the Home Computers.
Another recipe for the success of the PC might be, that there have been multiple CPU vendors for the same architecture (x86), like Intel, AMD, Cyrix, Via or IBM.
Internet of Things
The Internet was originally designed to connect military institutions in an redundant way, so if one net element fails, the rest would be still operable.
The bandwidth available evolves like compute power, exponentially, at first mainly text was submitted, like emails (1970s) or newsgroups (1980s), followed by web-pages with images via the World Wide Web (1989) or Gopher (1991), audio as .mp3 (~1995), and finally, Full HD videos via streaming platforms like YouTube or Netflix.
In the late 1990s, mobile-phones like the Nokia Communicator, MP3 audio players, PDAs, (Personal Digital Assistants) like the Palm Pilots and digital cameras marked the rise of the Smart Devices.
Their functions were all united into the Smart-Phone, and with mobile, high-bandwidth internet it is still on its triumph tour across the globe.
I am not able to portrait the current state of computer and internet usage, it is simply too omnipresent, from word-processing to AI-research, from fake-news to dark-net, from botnets of webcams to data-leaks in toys...
The next thing
but i can guess what the next step will be, Integrated Devices, the BCI, the Brain Computer Interface, connected via the Internet to an real kind of Matrix.
It seems only logical to conclude that we will connect with machines directly, implant chips, or develop non-invasive scanners, so the next bandwidth demand will be brainwaves, in all kind of forms.