Vortices in 2D p+ip superconductors/superfluids can support localized eigenstates with eigenenergy exactly zero. In addition, if the system is spin-polarized (spinless), the second-quantized operators for these zero-energy states are self-hermitian Majorana operators. It takes a pair of vortices (a pair of Majorana fermions) to accommodate a single quasiparticle of the superconductor. If the vortices are spatially well-separated, this  accommodation is manifestly non-local. Furthermore, the Majorana fermions endow the vortices with a braiding statistics which is non-Abelian. In contrast to the usual anyonic (Abelian) statistics, where the many-particle wavefunction acquires just a phase factor under pairwise interchange of coordinates, for non-Abelian statistics the wavefunction transforms as a vector in a finite-dimensional Hilbert space in such a process. Based on these two key properties, non-locality and non-Abelian statistics, we have recently proposed to use the 2D p+ip condensate, either in optical traps or in real materials such as strontium ruthenate, as a platform for topological quantum computation. In this talk, I shall describe this proposal clarifying the origin of the zero-energy states both in the BdG framework and more robustly from an Index Theorem, clarifying the non-Abelian statistics and the topological ground state degeneracy, and discussing how these can be accessed and implementated in optical traps and (possibly) in strontium ruthenate.