  We review here {\it Maximum Caliber} (Max Cal), a general variational
principle for inferring distributions of paths in dynamical processes and
networks. Max Cal is to dynamical trajectories what the principle of {\it
Maximum Entropy} (Max Ent) is to equilibrium states or stationary populations.
In Max Cal, you maximize a path entropy over all possible pathways, subject to
dynamical constraints, in order to predict relative path weights. Many
well-known relationships of Non-Equilibrium Statistical Physics -- such as the
Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations,
and Prigogine's Minimum Entropy Production -- are limited to near-equilibrium
processes. Max Cal is more general. While it can readily derive these results
under those limits, Max Cal is also applicable far from equilibrium. We give
recent examples of MaxCal as a method of inference about trajectory
distributions from limited data, finding reaction coordinates in bio-molecular
simulations, and modeling the complex dynamics of non-thermal systems such as
gene regulatory networks or the collective firing of neurons. We also survey
its basis in principle, and some limitations.
