  We present a pedagogical discussion of the Coriolis field, emphasizing its
not-so-well-understood aspects. We show that this field satisfies the field
equations of the so-called Newton-Cartan theory, a generalization of Newtonian
gravity that is covariant under changes of arbitrarily rotating and accelerated
frames. Examples of solutions of this theory are given, including the Newtonian
analogue of the G\"odel universe. We discuss how to detect the Coriolis field
by its effect on gyroscopes, of which the gyrocompass is an example. Finally,
using a similar framework, we discuss the Coriolis field generated by mass
currents in general relativity, and its measurement by the Gravity Probe B and
LAGEOS/LARES experiments.
