  The observation of the motion of particles and light near a gravitating
object is until now the only way to explore and to measure the gravitational
field. In the case of exact black hole solutions of the Einstein equations the
gravitational field is characterized by a small number of parameters which can
be read off from the observables related to the orbits of test particles and
light rays. Here we review the state of the art of analytical solutions of
geodesic equations in various space--times. In particular we consider the four
dimensional black hole space--times of Pleba\'nski--Demia\'nski type as far as
the geodesic equation separates, as well as solutions in higher dimensions, and
also solutions with cosmic strings. The mathematical tools used are elliptic
and hyperelliptic functions. We present a list of analytic solutions which can
be found in the literature.
