  Among several models for microswimmers, the three-sphere microswimmer
proposed by Najafi and Golestanian captures the essential mechanism for the
locomotion of a microswimmer in a viscous fluid. Owing to its simplicity and
flexibility, the original three-sphere model has been extended and generalized
in various ways to discuss new swimming mechanisms of microswimmers. We shall
provide a systematic and concise review of the various extensions of the
three-sphere microswimmers that have been developed by the present authors. In
particular, we shall discuss the following seven cases; elastic, thermal, odd,
autonomous three-sphere microswimmers; two interacting ones; and those in
viscoelastic and structured fluids. The well-known Purcell's scallop theorem
can be generalized for stochastic three-sphere microswimmers and also for the
locomotion in viscoelastic and structured fluids.
