Sea level, the height of the ocean surface at any given location, is de�ned either with respect to the surface of the solid Earth (relative sea level) or to a geocentric reference such as the reference ellipsoid. The former is the more relevant quantity when considering the coastal impacts of sea level change. Relative sea level has been measured using tide gauges during the past few centuries and estimated for longer time spans from geological records, while geocentric sea level has been observed over the past two decades only using satellite altimetry. Changes in sea level represent an integration of many aspects of climate change, and thus occur over a broad range of temporal and spatial scales. Many processes contribute to sea level variability and change, being associated with changes in the ocean, changes in the atmosphere and changes in the solid Earth. Understanding these processes better requires a consistent and homogeneous data base of measured sea level. It is thus a viable objective to reconstruct past sea levels by combining the long, but relatively sparse, time series of tide gauge observations with the shorter, but spatially dense, data set from altimetry and/or data-assimilated ocean models. Solving this problem essentially represents an extrapolation problem. A number of methods has been developed to this end in the past, typically based on extracting dominating patterns of sea level from the altimetry era in a �rst step.