Engineers design structures are often expected to withstand extreme environmental loads. In the context of offshore engineering, such loads are due largely to very high waves and winds that occur relatively infrequently. A critical aspect of design therefore consists of estimating environmental conditions with a low probability of occurrence or a high “return period.” The estimation of such conditions is reviewed in this article. While some commonly used techniques have been described in earlier review papers and books, this article provides a primer (in the early part which describes the basic methodology and commonly used distributions) and also summarizes many recent developments that are now in vogue. In particular, salient features of the following are described: new tools for parameter estimation, distributions such as the generalized extreme value and the Pareto distributions that were hitherto not commonly used, methods to incorporate trends in the data (e.g., from the viewpoint of climate change and sea level rise), methods to use multiple maxima in the data sets, modeled global data sets that have become widely available, and new software for obtaining the desired estimates efficiently. These advances, along with an understanding of various associated difficulties, can help the engineer make more informed choices regarding the estimation of extreme conditions for design.