  Undulatory locomotion is a means of self-propulsion that relies on the
generation and propagation of waves along a body. As a mode of locomotion it is
primitive and relatively simple, yet can be remarkably robust. No wonder then,
that it is so prevalent across a range of biological scales from motile
bacteria to gigantic prehistoric snakes. Key to understanding undulatory
locomotion is the body's interplay with the physical environment, which the
swimmer or crawler will exploit to generate propulsion, and in some cases, even
to generate the underlying undulations. This review focuses by and large on
undulators in the low Reynolds numbers regime, where the physics of the
environment can be much more tractable. We review some key concepts and
theoretical advances, as well as simulation tools and results applied to
selected examples of biological swimmers. In particular, we extend the
discussion to some simple cases of locomotion in non-Newtonian media as well as
to small animals, in which the nervous system, motor control, body properties
and the environment must all be considered to understand how undulations are
generated and modulated. To conclude, we review recent progress in microrobotic
undulators that may one day become commonplace in applications ranging from
toxic waste disposal to minimally invasive surgery.
