  Quantum networks are often modelled using Schroedinger operators on metric
graphs. To give meaning to such models one has to know how to interpret the
boundary conditions which match the wave functions at the graph vertices. In
this article we give a survey, technically not too heavy, of several recent
results which serve this purpose. Specifically, we consider approximations by
means of ``fat graphs'' -- in other words, suitable families of shrinking
manifolds -- and discuss convergence of the spectra and resonances in such a
setting.
