Coastal subsidence contributes to relative sea-level rise and exacerbates flooding hazards, with the at-risk population expected to triple by 2070. Natural processes of vertical land motion, such as tectonics, glacial isostatic adjustment and sediment compaction, as well as anthropogenic processes, such as fluid extraction, lead to globally variable subsidence rates. In this Review, we discuss the key physical processes driving vertical land motion in coastal areas. Use of space-borne and land-based techniques and the associated uncertainties for monitoring subsidence are examined, as are physics-based models used to explain contemporary subsidence rates and to obtain future projections. Steady and comparatively low rates of subsidence and uplift owing to tectonic processes and glacial isostatic adjustment can be assumed for the twenty-first century. By contrast, much higher and variable subsidence rates occur owing to compaction associated with sediment loading and fluid extraction, as well as large earthquakes. These rates can be up to two orders of magnitude higher than the present-day rate of global sea-level rise. Multi-objective predictive models are required to account for the underlying physical processes and socio-economic factors that drive subsidence. Measuring coastal subsidence is essential to evaluating hazards associated with sea-level rise. This Review discusses the processes driving coastal subsidence, space-borne and land-based measurement techniques, as well as models for simulating observed subsidence and predicting future trends.