  The edges of time reversal symmetry breaking topological superconductors
support chiral Majorana bound states as well as spontaneous charge currents.
The Majorana modes are a robust, topological property, but the charge currents
are non-topological--and therefore sensitive to microscopic details--even if we
neglect Meissner screening. We give insight into the non-topological nature of
edge currents in chiral p-wave superconductors using a variety of theoretical
techniques, including lattice Bogoliubov-de Gennes equations, the
quasiclassical approximation, and the gradient expansion, and describe those
special cases where edge currents do have a topological character. While edge
currents are not quantized, they are generically large, but can be
substantially reduced for a sufficiently anisotropic gap function, a scenario
of possible relevance for the putative chiral p-wave superconductor
Sr$_2$RuO$_4$.
