Submarine permafrost is perennially cryotic earth material that lies offshore. Most submarine permafrost is relict terrestrial permafrost beneath the Arctic shelf seas, was inundated after the last glaciation, and has been warming and thawing ever since. As a reservoir and confining layer for gas hydrates, it has the potential to release greenhouse gasses and impact coastal infrastructure, but its distribution and rate of thaw are poorly constrained by observational data. Lengthening summers, reduced sea ice extent and increased solar heating will increase water temperatures and thaw rates. Observations of gas release from the East Siberian shelf and high methane concentrations in the water column and air above it have been attributed to flowpaths created in thawing permafrost. In this context, it is important to understand the distribution and state of submarine permafrost and how they are changing. We assemble recent and historical drilling data on regional submarine permafrost degradation rates and review recent studies that use modelling, geophysical mapping and geomorphology to characterize submarine permafrost. Implications for submarine permafrost thawing are discussed within the context of methane cycling in the Arctic Ocean and global climate change.