  Spectral properties of Schr\"odinger operators on compact metric graphs are
studied and special emphasis is put on differences in the spectral behavior
between different classes of vertex conditions. We survey recent results
especially for $\delta$ and $\delta'$ couplings and demonstrate the spectral
properties on many examples. Amongst other things, properties of the ground
state eigenvalue and eigenfunction and the spectral behavior under various
perturbations of the metric graph or the vertex conditions are considered.
