  We describe how to characterize dynamical phase transitions in open quantum
systems from a purely dynamical perspective, namely, through the statistical
behavior of quantum jump trajectories. This approach goes beyond considering
only properties of the steady state. While in small quantum systems dynamical
transitions can only occur trivially at limiting values of the controlling
parameters, in many-body systems they arise as collective phenomena and within
this perspective they are reminiscent of thermodynamic phase transitions. We
illustrate this in open models of increasing complexity: a three-level system,
a dissipative version of the quantum Ising model, and the micromaser. In these
examples dynamical transitions are accompanied by clear changes in static
behavior. This is however not always the case, and in general dynamical phase
behavior needs to be uncovered by observables which are strictly dynamical,
e.g. dynamical counting fields. We demonstrate this via the example of a class
of models of dissipative quantum glasses, whose dynamics can vary widely
despite having identical (and trivial) stationary states.
