CDC was originally formed by thirteen members of the Sperry Rand Univac computer division. They had originally been the founding members of another company, Engineering Research Associates, who had formed to build code-breaking machinery for the US Navy. The company was purchased by Sperry Rand in 1952 after a series of political debates about the Navy essentially "owning" ERA, and Sperry was quick to use their drum memory products in other lines. It was not long before the core of the ERA team got fed up with Sperry Rand and decamped.
Of the members forming CDC, William Norris was the unanimous choice to become CEO, and Seymour Cray as their chief engineer. CDC started business by selling parts, mostly drum systems, to other companies.
Meanwhile they were also designing their own computer under the leadership of Cray. This design was eventually released as the CDC 1604 in 1958, with the first delivered to the US Navy in 1960. At the time it was one of the most powerful computers in the world, as well as one of the first to be built primarily from transistors.
However this was only the starting point. Cray had already moved on to the design of what would become the CDC 6600, a machine of far greater power. The 6600 had a simple CPU, but used a series of external I/O processors to offload many common tasks. That way the CPU could devote all of its time and circuitry to processing data while the other controllers dealt with mundane tasks like punching cards and running disks which would otherwise tie up the CPU.
The 6600 completely outperformed all machines on the market, typically by over ten times. It retained this leadership position until 1969 when it was finally outdone by its own designer. Using late-model compilers the machine still racks up .5 MFlops, impressive considering that it is about 30 years old.
It was at this point that IBM took notice. At the time Thomas Watson asked (paraphrased) how is it that this tiny company of 20 people can be beating us when we have thousands of people?, to which Cray replied you just answered your own question.
In 1965 IBM started an effort to build their own machine that would be even faster than the 6600, the ASCC. 200 people were sent to the west coast to run the project away from corporate prodding, at which point nothing happened. ASCC was eventually cancelled in 1969 after producing nothing, and 190 of the 200 employees stayed on the coast rather than suffer being recalled to IBM in New York.
But in the short term IBM also went ahead and announced a new version of the famed System/360 that would be just as fast as the 6600. This machine didn't exist, but that didn't stop sales of the 6600 drying up while people waited for its release – a tactic known today as FUD and more commonly associated with Microsoft. Norris didn't take this lying down, and a year later filed an anti-trust suit against IBM, eventually winning over 600 million dollars and picking up several parts of IBM's empire in the process.
The same month they won they also announced their own new machine, the CDC 7600. Cray had started the design quite a bit earlier and allowed it to mature fully. This machine ran at about five times the speed of the 6600, yet it was almost perfectly backward compatible. Much of this speed increase was due to extensive use of pipelining, a technique that allows different parts of the CPU to work on different parts of the instruction processs at the same time.
Once again Cray had started the next design before the last shipped. The CDC 8600 was to be a 4-processor unit in a case much smaller than the 7600 it would replace, the smaller size allowing for shorter delays and a faster clock cycle. However by 1972 Cray had become fed up working for what was now a very big company, and left to form Cray Research. Norris remained a staunch supporter of Cray, and even invested money into his new company.
At the same time as the 8600 effort, CDC had another project called Star underway. Unlike the 8600's "put four 7600's in a box" solution to the speed problem, the Star was a new design using a technique we know today as a vector processor. Eventually the 8600 was cancelled in 1974, and the Star would go on to become the Cyber 200. Several updates to the Cyber design were released through the 1970's.
But by this time Cray's own designs like the Cray-1 were using the same design techniques as the Cyber, yet doing it much faster. Meanwhile several very large Japanese manufacturing firms were entering the market as well. The supercomputer market was too small to be able to afford more than a handful of players, and CDC started looking for other markets. By 1992, the original Control Data Corporation ceased to exist as a computer hardware manufacturer and became known as Control Data Systems, Inc., with the non-computer business becoming Ceridian.