  Resonance and decay phenomena are ubiquitous in the quantum world. To
understand them in their complexity it is useful to study solvable models in a
wide sense, that is, systems which can be treated by analytical means. The
present review offers a survey of such models starting the classical Friedrichs
result and carrying further to recent developments in the theory of quantum
graphs. Our attention concentrates on dynamical mechanism underlying resonance
effects and at time evolution of the related unstable systems.
