Fracton topological phases represent a new kind of three-dimensional topological order that is characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy.  Apart from providing an intriguing alternative to Bose or Fermi statistics in three dimensions, these phases are of interest as possibly robust quantum memories and for their "glassy" dynamical behavior.  After describing the phenomenology of these phases, we present systematic ways of searching for and characterizing these topological phases by (i) invoking a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems and (ii) by coupling together an isotropic array of two-dimensional topological phases.  We conclude by presenting solvable models that describe "non-Abelian" generalizations of these three-dimensional phases, where the point-like excitations carry a protected, internal degeneracy that may be manipulated.