Majorana zero modes are fermion-like excitations that were originally proposed in particle physics by Ettore Majorana and are characterized as being their own anti-particle. In condensed matter systems Majorana zero modes occur as fractionalized excitations with topologically protected degeneracy associated with such excitations. For over a decade the only candidate systems for observing Majorana zero modes were the non-Abelian fractional quantum Hall state and chiral p-wave superconductors. In this talk, I will discuss theoretical understanding of the results from the experimental search for Majorana zero modes in spin-orbit coupled semiconductor-based topological superconducting systems. Following this I will discuss future possibilities in terms of modifications to the experiments to help confirm the presence of Majorana zero modes through more dramatic signatures.