  We present a numerical implementation of the geodesic ray transform and its
inversion over functions and solenoidal vector fields on two-dimensional
Riemannian manifolds. For each problem, inversion formulas previously derived
in \cite{Pestov2004,Krishnan2010} are implemented in the case of simple and
some non-simple metrics. These numerical tools are also used to better
understand and gain intuition about non-simple manifolds, for which injectivity
and stability of the corresponding integral geometric problems are still under
active study.
