  We discuss the locomotion of a three-sphere microswimmer in a viscoelastic
structured fluid characterized by typical length and time scales. We derive a
general expression to link the average swimming velocity to the sphere
mobilities. In this relationship, a viscous contribution exists when the
time-reversal symmetry is broken, whereas an elastic contribution is present
when the structural symmetry of the microswimmer is broken. As an example of a
structured fluid, we consider a polymer gel, which is described by a
"two-fluid" model. We demonstrate in detail that the competition between the
swimmer size and the polymer mesh size gives rise to the rich dynamics of a
three-sphere microswimmer.
