Two-dimensional superconductors with broken time-reversal symmetry have been predicted to support topologically protected chiral edge states, providing a thermal analogue of the electrical quantum Hall effect in semiconductors. Several decades of search for these edge states (notably in strontium ruthenate) have not yet produced convincing evidence for their existence. The key difficulty is that the edge states are charge neutral, and therefore would seem to be out reach of conventional electrical probes. Here we discuss some recent developments in our understanding of the Majorana nature of the superconducting edge states, which suggests that shot noise measurements would provide for a purely electrical method of detection.