  We review our understanding of the kinematics of the LMC and the SMC, and
their orbit around the Milky Way. The line-of-sight velocity fields of both the
LMC and SMC have been mapped with high accuracy using thousands of discrete
traces, as well as HI gas. The LMC is a rotating disk for which the viewing
angles have been well-established using various methods. The disk is elliptical
in its disk plane. The disk thickness varies depending on the tracer
population, with V/sigma ranging from 2-10 from the oldest to the youngest
population. For the SMC, the old stellar population resides in a spheroidal
distribution with considerable line-of-sight depth and low V/sigma. Young stars
and HI gas reside in a more irregular rotating disk. Mass estimates based on
the kinematics indicate that each Cloud is embedded in a dark halo. Proper
motion measurements with HST show that both galaxies move significantly more
rapidly around the Milky Way than previously believed. This indicates that for
a canonical 10^12 solar mass Milky Way the Clouds are only passing by us for
the first time. Although a higher Milky Way mass yields a bound orbit, this
orbit is still very different from what has been previously assumed in models
of the Magellanic Stream. Hence, much of our understanding of the history of
the Magellanic System and the formation of the Magellanic Stream may need to be
revised. The accuracy of the proper motion data is insufficient to say whether
or not the LMC and SMC are bound to each other, but bound orbits do exist
within the proper motion error ellipse.
