The estimation of extreme significant wave heights Hs using altimeter observations is investigated. Data from the following three satellite missions are used: Geosat, ERS-1 and Topex/Poseidon. Practical methods of estimating extreme Hs are described and limitations of their application to altimeter data are highlighted. Extreme Hs are estimated using the three-parameter Weibull distribution, with maxima selected via the peaks over threshold method, and the Fisher-Tippet type I distribution, using data selected via the initial distribution method. Altimeter estimates are compared to extreme Hs calculated from deep water buoy data. A comparative analysis of global estimates of satellite-derived extreme Hs based on standard statistics investigates time-space undersampling and how it affects the reliability of long-term extreme wave estimates made using satellite altimeter data.