This chapter describes the use of electron spins in semiconductor quantum dots as quantum bits for quantum information processing. Among the central themes of the chapter is the mechanism for a two-qubit operation based on the exchange interaction. Another important topic pertains to the mechanisms that lead to the loss of quantum coherence and are related to phonons or nuclear spins in the host semiconductor. The last part of this chapter is focused on the prospects for extending the ideas of spin-based quantum information to new materials such as graphene, where both nuclear-spin- and phonon-induced decoherence and relaxation are suppressed.