Summary: A recent spate of research has attempted to develop estimators for stochastic frontier models that embrace semi- and nonparametric insights to enjoy the advantages inherent in the more traditional operations research method of data envelopment analysis. These newer methods explicitly allow statistical noise in the model, the absence of which is a common criticism of the data envelopment estimator. Further, several of these newer methods have focused on ensuring that axioms of production hold. These models and their subsequent estimators, despite having many appealing features, have yet to appear regularly in empirical research. Given the pace at which estimators of this style are being proposed, coupled with the dearth of formal applications, we seek to review the literature and discuss practical implementation issues of these methods. We provide a general overview of the major recent developments in this important arena, draw connections with the data envelopment analysis field, and discuss how useful synergies can be undertaken. We also include simulations comparing the performance of many of the methods presented here.