  We give a short review of results on inverse spectral problems for ordinary
differential operators on a spatial networks (geometrical graphs). We pay the
main attention to the most important nonlinear inverse problems of recovering
coefficients of differential equations from spectral characteristics provided
that the structure of the graph is known a priori. In the first half of the
review we provide results related to inverse Sturm-Liouville problems on
arbitrary compact graphs. Further, results on inverse problems for arbitrary
order differential operators on compact graphs are presented. At the end we
provide the main results on inverse problems on noncompact graphs.
