We review the theoretical proposal for quantum computing with electron spins in quantum confined structures and discuss the essential requirements for its implementation. The quantum bit is represented by the spin of the electron, as opposed to the charge (orbital) degrees of freedom. In this context, we analyze a number of physical realizations of the elementary building blocks for quantum computation: a universal set of quantum gates, state preparation and measurement. Finally, we discuss the production, transport, and detection of electronic Einstein-Podolski-Rosen pairs, which are an important resource for quantum communication.