The measurement of efficiency in higher education has gained a growing interest in recent years, especially due to the expansion of the university system. This paper provides a review of the literature on efficiency in higher education institutions by covering empirical articles which applied frontier efficiency measurement techniques from 1997 to 2019. We review the methodological approaches used, both parametric and non-parametric techniques, such as Data Envelopment Analysis, Malmquist index and Stochastic Frontier Analysis. Secondly, we list the applied inputs, input prices, outputs, quality, and environment variables and based on the overview, we discuss the advantages and drawbacks of the different empirical proxy variables used. We address the importance of characterizing students and research funding as raw materials of both the teaching and research services, respectively, and we provide suggestions on how to deal with them empirically. We also discuss the difference between quality and environmental variables, and we give some practical indications to distinguish them in doubtful cases.