Abelian gerbes play a ubiquitous role in string and supergravity theories. It is conjectured that non-abelian gerbe theories exist, but a satisfactory explicit construction of such a theory has not yet been achieved. Inspired by the possibility that a non-abelian theory of gerbes may be possible on non-conventional spacetimes, I will consider a toy model on a lattice that allows one to make some progress in this problem. In this talk, I will show how abelian gerbe theories may be described naturally on the lattice. I will outline a non-abelian generalisation and show how, under dimensional reduction, such theories give rise to lattice Yang-Mills.