Fusion categories appear in many areas of mathematics. They are realized by topological quantum field theories, representations of finite groups and Hopf algebras, and invariants for knots and Murray-von Neumann subfactors. An important numerical invariant of these categories are the Frobenius-Schur indicators, which are generalized versions of those for finite group representations. Using these categorical indicators we are able to distinguish near-group fusion categories, that is those fusion categories with one non-invertible object, and obtain some realizations of their tensor equivalence classes.