I will first give a general background to topological field theories, with emphasis on the BF description of superconductors. In the second part of the talk I will discuss a recently proposed topological field theory for a spinless 2D chiral superconductor that contains fundamental Majorana fields. Due to a local fermionic symmetry, the Majorana modes survive as dynamical degrees of freedom only at vortex cores, and on edges. I will discuss the statistics of the vortices, the edge modes and the ground state degeneracy on the torus. If time allows I will also explain the connection to the Moore-Read Pfaan quantum Hall state, and extensions to three dimensions