  Cell motility in viscous fluids is ubiquitous and affects many biological
processes, including reproduction, infection, and the marine life ecosystem.
Here we review the biophysical and mechanical principles of locomotion at the
small scales relevant to cell swimming (tens of microns and below). The focus
is on the fundamental flow physics phenomena occurring in this inertia-less
realm, and the emphasis is on the simple physical picture. We review the basic
properties of flows at low Reynolds number, paying special attention to aspects
most relevant for swimming, such as resistance matrices for solid bodies, flow
singularities, and kinematic requirements for net translation. Then we review
classical theoretical work on cell motility: early calculations of the speed of
a swimmer with prescribed stroke, and the application of resistive-force theory
and slender-body theory to flagellar locomotion. After reviewing the physical
means by which flagella are actuated, we outline areas of active research,
including hydrodynamic interactions, biological locomotion in complex fluids,
the design of small-scale artificial swimmers, and the optimization of
locomotion strategies.
