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The abacus was thought to have been invented in Babylon c. 2700–2300 BC. Its original style of usage was by lines drawn in sand with pebbles. Abaci, of a more modern design, are still used as calculation tools today. This was the first known calculator and most advanced system of calculation known to date - preceding Archimedes by 2,000 years.

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In c. 1050–771 BC, the south-pointing chariot was invented in ancient China. It was the first known geared mechanism to use a differential gear, which was later used in analog computers. The Chinese also invented a more sophisticated abacus from around the 2nd century BC known as the Chinese abacus.

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Difference engine and the Analytical engine

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Difference engine and the Analytical engine

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Indeed, when John Napier discovered logarithms for computational purposes in the early 17th century, there followed a period of considerable progress by inventors and scientists in making calculating tools. The apex of this early era of formal computing can be seen in the difference engine and its successor the analytical engine (which was never completely constructed but was designed in detail), both by Charles Babbage. The analytical engine combined concepts from his work and that of others to create a device that if constructed as designed would have possessed many properties of a modern electronic computer. These properties include features such as an internal "scratch memory" equivalent to RAM, multiple forms of output including a bell, a graph-plotter, and simple printer, and a programmable input-output "hard" memory of punch cards which it could modify as well as read. The key advancement which Babbage's devices possessed beyond those created before his was that each component of the device was independent of the rest of the machine, much like the components of a modern electronic computer. This was a fundamental shift in thought; previous computational devices served only a single purpose, but had to be at best disassembled and reconfigured to solve a new problem. Babbage's devices could be reprogramed to solve new problems by the entry of new data, and act upon previous calculations within the same series of instructions.  Ada Lovelace took this concept one step further, by creating a program for the analytical engine to calculate Bernoulli numbers, a complex calculation requiring a recursive algorithm. This is considered to be the first example of a true computer program, a series of instructions that act upon data not known in full until the program is run. Following Babbage, although unaware of his earlier work, Percy Ludgate in 1909 published the 2nd of the only two designs for mechanical analytical engines in history.

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Eventually, vacuum tubes replaced relays for logic operations. Lee De Forest's modification, in 1907, of the Fleming valve can be used as a logic gate. Ludwig Wittgenstein introduced a version of the 16-row truth table as proposition 5.101 of Tractatus Logico-Philosophicus (1921). Walther Bothe, inventor of the coincidence circuit, got part of the 1954 Nobel Prize in physics, for the first modern electronic AND gate in 1924. Konrad Zuse designed and built electromechanical logic gates for his computer Z1 (from 1935–38).

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The first digital electronic computer was developed in the period April 1936 - June 1939, in the IBM Patent Department, Endicott, New York by Arthur Halsey Dickinson.In this computer IBM introduced for the first time, a calculating device with keyboard, processor and electronic output (display). Competitor to IBM was the digital electronic computer NCR3566, developed in NCR, Dayton, Ohio by Joseph Desch and Robert Mumma in the period April 1939 - August 1939.The IBM and NCR machines were decimal, executing addition and subtraction in binary position code.

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December 1939 John Atanasoff and Clifford Berry completed their experimental model to prove the concept of the Atanasoff–Berry computer.This experimental model is binary, executed addition and subtraction in octal binary code and is the first binary digital electronic computing device. The Atanasoff–Berry computer was intended to solve systems of linear equations, though it was not programmable and it was never completed.The Z3 computer, built by German inventor Konrad Zuse in 1941, was the first programmable, fully automatic computing machine, but it was not electronic.

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The ENIAC (Electronic Numerical Integrator And Computer) was the first electronic general-purpose computer, announced to the public in 1946. It was Turing-complete,[citation needed] digital, and capable of being reprogrammed to solve a full range of computing problems. Women implemented the programming for machines like the ENIAC, and men created the hardware.

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In terms of supercomputing, the first widely acknowledged supercomputer was the Control Data Corporation (CDC) 6600[66] built in 1964 by Seymour Cray. Its maximum speed was 40MHz or 3 million floating point operations per second (FLOPS). The CDC 6600 was replaced by the CDC 7600 in 1969;[67] although its normal clock speed was not faster than the 6600, the 7600 was still faster due to its peak clock speed, which was approximately 30 times faster than that of the 6600. Although CDC was a leader in supercomputers, their relationship with Seymour Cray (which had already been deteriorating) completely collapsed. in 1972, Cray left CDC and began his own company, Cray Research Inc.[68] With support from investors in Wall Street, an industry fueled by the Cold War, and without the restrictions he had within CDC, he created the Cray-1 supercomputer. With a clock speed of 80 MHz or 136 megaFLOPS, Cray developed a name for himself in the computing world. By 1982, Cray Research produced the Cray X-MP equipped with multiprocessing and in 1985 released the Cray-2, which continued with the trend of multiprocessing and clocked at 1.9 gigaFLOPS. Cray Research developed the Cray Y-MP in 1988, however afterwards struggled to continue to produce supercomputers. This was largely due to the fact that the Cold War had ended, and the demand for cutting edge computing by colleges and the government declined drastically and the demand for micro processing units increased.

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Today, supercomputers are still used by the governments of the world and educational institutions for computations such as simulations of natural disasters, genetic variant searches within a population relating to disease, and more. As of November 2020, the fastest supercomputer is Fugaku.