The location and shape of the magnetopause are among the important parameters in space physics because they specify the size of the magnetosphere and respond to the physical processes occurring therein. In the past few years, several empirical models of the magnetopause shape have been developed using large in situ data sets of magnetopause crossings. These models were derived from best-fits to observed magnetopause locations; however, the data sets, the functional forms of the magnetopause, and the specific dependence of the shape on the upstream solar wind conditions used by these models are different, so are their ranges of validity. In this paper, we provide a comprehensive review of these models, compare the differences among them, and discuss their limitations. In addition, we also show the results of validation of these models for space weather forecasts using the January 1997 magnetic cloud event.