Numerical models of surface tension play an increasingly important role in our capacity to understand and predict a wide range of multiphase flow problems. The accuracy and robustness of these models have improved markedly in the past twenty years, so that they are now applicable to complex, three-dimensional configurations of great theoretical and practical interest. In this review I attempt to summarize the most significant recent developments in Eulerian surface tension models, with an emphasis on well-balancing, curvature estimation, stability and implicit time-stepping as well as test cases and applications. The advantages and limitations of various models are discussed, with a focus on common features rather than differences. Several avenues for further progress are suggested.