As the version of Majorana fermions in condensed matter physics, the research of Majorana zero modes is one of the most interesting topics in physics currently. Majorana zero modes obey the non-Abelian statistics and can be used for constructing the topologically protected qubits. This kind of qubit constructed from spatially separated Majorana zero modes is immune to local noise, and has a long decoherence time, which makes it show important application prospects in fault-tolerant quantum computation. The semiconductor/superconductor nanowires are one of the most ideal experimental platforms for studying Majorana zero modes and topological quantum computation. This work reviews the research progress of the epitaxial growth of high-quality semiconductor nanowires, the fabrication of semiconductor/superconductor heterostructure nanowires, and Majorana zero modes in semiconductor/superconductor nanowires. The application prospects of semiconductor/ superconductor nanowires in quantum computation is also prospected finally.