Topological quantum matter has been an active research field in physics in the past three decades with numerous celebrated examples, including quantum Hall effect, chiral superconductor, topological insulator, etc. In topological materials, Majorana fermions, first envisioned by E. Majorana in 1935 to describe neutrinos, often emerge as topological quasiparticle excitations of the systems. Majorana fermions are intriguing because they can be construed as their own anti-particles and follow non-Abelian anyonic statistics under a pair-wise exchange of the many-particle wave function, unlike Dirac fermions where electrons and positrons (holes) are distinct. Although the emergence of Majorana fermions in any condensed matter or atomic system is by itself an extraordinary phenomenon, they have also come under a great deal of recent attention due to their potential use in fault tolerant quantum computation. In this talk, I will review recent theoretical and experimental progress on the search for Majorana fermions in two spin-orbit coupled systems: spin-orbit coupled degenerate Fermi gases and semiconductor/superconductor nanostructures. I will discuss the contribution of my group in this rapidly developing field.