The purpose of this survey paper is to paint the landscape of research on the efficiency profiles of Islamic banks and their Conventional counterparts with a focus on DEA studies. Such landscape is organised around classifications of types of measures of efficiency and their analyses, types of DEA analyses, types of DEA modelling frameworks and models, evaluation approaches and choice of variables for the specification of DEA models, and drivers of efficiency. To the best of our knowledge, no survey on the drivers of efficiency has ever been conducted. In this paper, we overcome this gap in the context of Islamic banking and backup previous findings with relevant theories. In addition, we unify the literature terminology-wise. Finally, a critical analysis of the literature is provided along with methodological gaps, inconsistencies, and future research directions.