DEA is a well-established, widely used, and powerful analytical resource in the toolbox of the OR/MS analyst. It is used to assess relative efficiency of many, functionally similar, entities. It has applications in diverse areas including finance and banking, education, and healthcare. DEA is computationally intensive and, as the scale of applications grows, this intensity rapidly becomes one of the limiting factors in its utility. In this paper, we explore computations in DEA. We investigate the theory behind schemes, procedures and algorithms used in performing a DEA study and we report on current practices ranging from the basic and standard to the advanced and sophisticated. Our objective is to give researchers and practitioners an appreciation for the computational aspects of DEA that will permit them to understand the performance, problems, complications, limitations, as well as the potential of this technique.