Extensive fields of sub-kilometre- to kilometre-scale mounds, cones, domes, shields, and flow-like edifices cover large parts of the martian lowlands. These features have been compared to structures on Earth produced by sedimentary volcanism – a process that involves subsurface sediment/fluid mobilisation and commonly releases methane to the atmosphere. It was proposed that such processes might help to explain the presence of methane in the martian atmosphere and may also have produced habitable, subsurface settings of potential astrobiological relevance. However, it remains unclear if sedimentary volcanism on Earth and Mars share genetic similarities and hence if methane or other gases were released on Mars during this process. The aim of this review is to summarise the current knowledge about mud-volcano-like structures on Mars, address the critical aspects of this process, identify key open questions, and point to areas where further research is needed to understand this phenomenon and its importance for the Red Planet's geological evolution. We show here that after several decades of exploration, the amount of evidence supporting martian sedimentary volcanism has increased significantly, but as the critical ground truth is still lacking, alternative explanations cannot be ruled out. We also highlight that the lower gravity and temperatures on Mars compared to Earth control the dynamics of clastic eruptions and surface emplacement mechanisms and the resulting morphologies of erupted material. This implies that shapes and triggering mechanisms of mud-volcano-like structures may be different from those observed on Earth. Therefore, comparative studies should be done with caution. To provide a better understanding of the significance of these abundant features on Mars, we argue for follow-up studies targeting putative sedimentary volcanic features identified on the planet's surface and, if possible, for in situ investigations by landed missions such as that by the Zhurong rover.