The emergence of topological order is one of the most intriguing 
phenomena in quantum many-body physics and one of possibly far 
reaching relevance -- topological quantum matter is increasingly 
appreciated as possible medium for quantum computation purposes. 
In this talk, I will discuss the stability of topological quantum 
matter when considering the effects of interactions and disorder 
on the collective quantum state formed by a set of topological 
excitations, so-called anyons. In particular, I will discuss the 
formation of a thermal metal of Majorana fermions in a 
two-dimensional system of interacting non-Abelian anyons in the 
presence of moderate disorder. This bulk metallic phase occurs 
for various proposed systems supporting Majorana fermion zero 
modes when disorder induces the random pinning of a finite density 
of vortices. This includes all two-dimensional topological 
superconductors in so-called symmetry class D. A distinct 
experimental signature of the thermal metal phase is the presence 
of bulk heat transport down to zero temperature. I will finish by 
discussing implications for topological quantum computing proposals.