Abstract: Mars does not have a global magnetic field of the internal origin, thus, the solar wind plasma can interact directly with the upper atmosphere and the ionosphere and be shocked with the mass-loading and magnetic pileup processes. Over the past decades, many studies have been conducted to understand the properties of the Martian bow shock and the major factors affecting the Martian bow shock, and develop models of the Martian bow shock, using the plasma and magnetic field measurements from Phobos 2, Mars Global Surveyor (MGS), and Mars Atmosphere and Volatile EvolutioN (MAVEN). In this brief review, we introduce the research progress of the Martian bow shock, with focus on the observational features, the major factors affecting the Martian bow shock, as well as the two-dimensional and three-dimensional Martian bow shock models. We also discuss some scientific questions that deserve further investigation in the future.