The geology of Mars and the stratigraphic characteristics of its uppermost crust (mega-regolith) suggest that some of the pervasively-occurring pitted cones, mounds, and flows may have formed through processes akin to terrestrial mud volcanism. A comparison of terrestrial mud volcanism suggests that equivalent Martian processes likely required discrete sedimentary depocenters, volatile-enriched strata, buried rheological instabilities, and a mechanism of destabilization to initiate subsurface flow. We outline five formational scenarios whereby Martian mud volcanism might have occurred: (A) rapid deposition of sediments, (B) volcano-induced destabilization, (C) tectonic shortening, (D) long-term, load-induced subsidence, and (E) seismic shaking. We describe locations within and around the Martian northern plains that broadly fit the geological context of these scenarios and which contain mud volcano-like landforms. We compare terrestrial and Martian satellite images and examine the geological settings of mud volcano provinces on Earth in order to describe potential target areas for piercement structures on Mars. Our comparisons help to evaluate not only the role of water as a functional component of geological processes on Mars but also how Martian mud volcanoes could provide samples of otherwise inaccessible strata, some of which could contain astrobiological evidence.