Peat is a highly compressible geological material whose time-dependent consolidation and rheological behaviour is determined by peat structure, degree of humification and hydraulic properties. This chapter reviews the engineering background to peat compression, describes the distribution of peat soils in the UK, provides examples of the hazards associated with compressible peat deposits and considers ways these hazards might be mitigated. Although some generalizations can be made about gross differences between broad peat types, no simple relationship exists between the magnitude and rate of compression of peat and loading. Based on examples described here, land failures resulting from peat compression are locally generated, but due to the sensitive nature of peat these can result in runaway failures that pose great risk. Understanding the geological hazards associated with compressible peat soils is challenging because peat is geotechnically highly variable and the mapped extent of peat in the UK is subject to considerable error due to inconsistencies in the definition of peat. Mitigating compression hazards in peat soils is therefore subject to considerable uncertainty; however, a combination of improved understanding of the properties of compressible peat, better mapping and land use zoning, and appropriate construction will help to mitigate risk.