The search for non-Abelian Majorana zero modes has become a most exciting research activity in condensed matter physics and also ultracold atoms in the recent decade. The studies advance our understanding of the fundamental physics in quantum matter and push forward the potential applications of such exotic states to topological quantum computation. In this colloquium I will review the recent progresses of search for Majorana modes and introduce our results in this topic. After a pedagogical introduction to the fundamentals of Majorana modes, I will introduce the experimental schemes for realization, focusing on the topological superconductors realized in spin-orbit coupled systems. The similar processes in ultracold atoms will also be assessed. Then I discuss the observation of Majorana modes, introduce the recent experimental studies, and point out challenges. Finally, we present a generic theory for the realization of non-Abelian Majorana modes, with which we show that such exotic modes can be obtained in much broader range of superconducting systems, topological or even trivial. Future issues in this exciting direction will be discussed.