Topological superconductors have attracted much research interest, because they were proposed to host non-abelian Ising Anyon Majorana zero modes and thus can be used to construct fault-tolerant topological quantum computers. This paper mainly reviews the electrical transport methods for detecting the presence of Majorana zero modes. First, the basic concepts of topological superconductivity, Majorana zero modes and non-Abelian statistics are introduced, followed by a summary of various schemes for implementing topological superconductivity. Then, the experimental methods for detecting topological superconductivity or Majorana zero modes by using low-temperature transport methods, including electron tunneling spectroscopy, Coulomb blockade spectroscopy and non-local conductance detection, which are widely used in superconductor/nanowire hybrid systems, are discussed. On the other hand, the measurements of the (inverse) AC Josephson effect and current (energy) phase relationships are also reviewed to identify Majorana zero modes in Josephson devices. Meanwhile, to deepen our understanding of Majorana zero modes, some mechanisms for explaining the experimental data observed in the above experiments are provided. Finally, a brief summary and outlook of the electrical transport methods of Majorana zero modes are presented.