  Analysis of black hole spacetimes requires study of the motion of particles
and light in these spacetimes. Here exact solutions of the geodesic equations
are the means of choice. Numerous interesting black hole spacetimes have been
analyzed in terms of elliptic functions. However, the presence of a
cosmological constant, higher dimensions or alternative gravity theories often
necessitate an analysis in terms of hyperelliptic functions. Here we review the
method and current status for solving the geodesic equations for the general
hyperelliptic case, illustrating it with set a of examples of genus $g=2$.
