What distinguishes topologically trivial from non-trivial superfluids in interacting many-body systems with a conserved number of particles? What is the meaning and fate of Majorana zero-energy modes in interacting fermionic superfluids? These are questions that require a concrete operational answer if one seriously considers using these physical systems for quantum information processing purposes. Most of what we know about topological superfluids and Majorana excitations is based on a mean-field approximation, the Bogoliubov-de Gennes approach, that breaks particle-number conservation and, by construction, displays a particle-hole symmetry and thus a zero mode structure. I will attempt to answer the questions above from both basic physics principles, and concrete models perspectives.