  Quantum mechanics is able to produce challenging behaviors even in the
simplest situations. This is possible because of the important dynamical role
that phase plays in the evolution of quantum systems, very similar,
nonetheless, to effects observable in analogous optical systems. The present
work focuses on how Bohmian mechanics proves to be a rather convenient
theoretical framework to analyze phase-based phenomena, since the phase
constitutes the central element in this hydrodynamical formulation of quantum
mechanics. More specifically, it allows us to understand how spatial phase
variations give rise to velocity fields that eventually rule the dynamical
behavior of quantum systems, and that, when integrated in time locally (i.e.,
taking into account specific positions), they provide us with a neat local
(point by point) description of the system evolution in the configuration
space. Indeed, it will also be seen that this idea transcends the quantum realm
and can be profitably used to describe the behavior of optical analogs with
rather singular behaviors. With this purpose, two interesting phenomena that
take place in free space are considered, namely, the self-acceleration and
shape-invariance of Airy beams, and spontaneous self-focusing.
