Complex systems often defy direct solution and analysis. One consequence of this is that computers, typically digital computers, have played a key role in advancing our understanding of complex and nonlinear systems. The history of computer technology, especially in the early years, reveals a number of examples where there was a close interplay between the use and development of computers and the study of complex systems. The mathematicians John von Neumann, Stanislaw Ulam, and their colleagues published work in the 1940s and 1950s on their digitial computer studies of nonlinear problems, including deterministic chaos, that used the newly available computers at Los Alamos Scientific Laboratory .

ENIAC (Electrical Numerical Integrator And Calculator) is usually given the honor of being called the first electronic programmable computer. Its construction was completed in 1946 under the direction of J. Presper Eckert and John Mauchly at the Moore School of Electrical Engineering of the University of Pennsylvania. It was built out of about 18,000 vacuum tubes, was physically quite large, covering something like 2,000 square feet of floor space, and in operation consumed 200 kilowatts of power. It was programmed by plugging together its different functional units (adders, multipliers, and accumulators).

In 1943 Alan Turing 's group in England built Colossus, also an electronic programmable computer, and some feel that Turing's machine should be called the first.

Electronic stored-program computers didn't appear until after John von Neumann's study of how to build machines that didn't require hand programming, but that could select and load-in programs automatically. One of the first of these was the EDVAC.