The 1900s

1912: The Institute of Radio Engineers was founded -- the second organization that would eventually merge to found the IEEE in 1963.

1925: Babbage's and Hollerith's digital computing methods were rarely used in scientific computation, though analog devices such as the slide rule were in wide use, especially in engineering calculations. Vannevar Bush, MIT, built a large-scale differential analyzer with the additional capabilities of integration and differentiation. Funded by the Rockefeller Foundation, the differential analyzer was perhaps the largest computational device in the world in 1930.

Digital computing came to the fore again in the 1930's when a number of scientists recognized that the technology had reached the stage where the necessary components of a computer were available. Each, in his turn, had to conceive (or perhaps "reconceive" not being aware of the prior work of Babbage) of the structure of a computer.
1935-38: Konrad Zuse, in Berlin, Germany, developed his Z-1 computer in his parents' living room, a relay computer, using binary arithmetic. He continued with the Z-2 in 1938 with the help of Helmut Schreyer. During World War II he applied to the German Government for assistance in building his machines, but he was turned down on the basis that it would take longer to complete his work than the government expected the war to last. Eventually he fled to Hinterstein  at the end of the war and then to Switzerland where he reconstructed his Z-4 machine at the University of Zurich and founded a computer company that was eventually absorbed into the Siemens Corporation.

1936-39: John Vincent Atanasoff, with John Berry, developed the machine we now call  the ABC -- the Atanasoff-Berry Computer -- at Iowa State University, USA as a special purpose machine for the solution of sets of linear equations in Physics. Perhaps the earliest example of an electronic calculator, the ABC did develop primary concepts that would appear later in "modern computers" -- the electronic arithmetic unit and the regenerative, cyclic memory.

1937: While not using the practical technology of the era, Alan Turing developed the idea of a "Universal Machine" capable of executing any describable algorithm, and forming the basis for the concept of "computability".

Also in the US two other people were considering the problems of computation: Howard Aiken at Harvard University, whose work would come to fruition in 1944, and George Stibitz at Bell Telephone Laboratories who was looking at the use of telephone relays in doing arithmetic. He first constructed a relay driven arithmetic unit in 1937 (which he later called the Model-K since it was built on the Kitchen table) and from that small start built a number of relay machines that were in use during World War II.

1939: One of the major computational problems at Bell Telephone Laboratories was in the domain of complex numbers. Stibitz' first full-scale electromagnetic relay calculator solved this problem and was named the Complex Number Calculator. A year later this machine was the first to be used remotely over telephone lines, setting the stage for the linking of computers and communication systems, time-sharing, and eventually networking.