Upon their discovery in 2000, Martian gullies were hailed as the first proof of recent (i.e. less than a few million years) flowing liquid water on the surface of a dry desert planet. Many processes have been proposed to have formed Martian gullies, ranging from liquid-water seepage from aquifers, melting of snow, ice and frost, to dry granular flows, potentially lubricated by CO₂. Terrestrial analogues have played a pivotal role in the conception and validation of gully-formation mechanisms. Comparison with the terrestrial landscape argues for gully formation by liquid-water debris flows originating from surface melting. However, limited knowledge of sediment transport by sublimation is a critical factor in impeding progress on the CO₂-sublimation hypothesis. We propose avenues towards resolving the debate: (a) laboratory simulations targeting variables that can be measured from orbit; (b) applications of landscape-evolution models; (c) incorporation of the concept of sediment connectivity; (d) using 3D fluid-dynamic models to link deposit morphology and flow rheology; and (e) a more intense exchange of techniques between terrestrial and planetary geomorphology, including quantitative and temporal approaches. Finally, we emphasize that the present may not accurately represent the past and that Martian gullies likely formed by a combination of processes.