The ability to store and execute lists of instructions called programs makes computers extremely versatile and distinguishes them from calculators. The Church–Turing thesis is a mathematical statement of this versatility: any computer with a certain minimum capability is, in principle, capable of performing the same tasks that any other computer can perform. Therefore, computers with capability and complexity ranging from that of a personal digital assistant to a supercomputer are all able to perform the same computational tasks given enough time and storage capacity.

It is difficult to identify any one device as the earliest computer, partly because the term "computer" has been subject to varying interpretations over time. Originally, the term "computer" referred to a person who performed numerical calculations (a human computer), often with the aid of a mechanical calculating device.
The history of the modern computer begins with two separate technologies - that of automated calculation and that of programmability.
Examples of early mechanical calculating devices included the abacus, the slide rule and arguably the astrolabe and the Antikythera mechanism (which dates from about 150-100 BC). Hero of Alexandria (c. 10–70 AD) built a mechanical theater which performed a play lasting 10 minutes and was operated by a complex system of ropes and drums that might be considered to be a means of deciding which parts of the mechanism performed which actions and when. This is the essence of programmability.