Background: Over the past decade, there has been a shift in science, technology, engineering and math education, especially in engineering, towards a competency-based pedagogy. Competency-based learning (CBL) is an outcome-based, student-centered form of instruction where students progress to more advanced work upon mastering the necessary prerequisite content and skills. Many articles have been published on the implementation of CBL in engineering higher education; however, the literature lacks a systematic review that summarizes prior work to inform both future research and practice. Purpose: The purpose of this review is to integrate previous literature as well as identify gaps in competency-based engineering higher education research. It summarizes the different approaches for implementing CBL, the effects of the pedagogy on student outcomes, tools to enhance its effectiveness, and assessment strategies. In addition, suggestions and recommendations for future research are provided. Method: Engineering education articles were obtained from several EBSCO educational databases. The search was limited to articles published from 2005-2015, and inclusion criteria consisted of peer-reviewed journal articles that address the use of CBL in engineering higher education. Articles were then classified into several categories, summarized, and evaluated. Conclusions: Theoretical and applied perspectives are provided that address both the theoretical basis for the effectiveness of CBL and practical aspects of implementing successful CBL instruction in engineering education. There are gaps in the literature regarding how CBL programs should be structured and assessed. Future research directions include empirical quantitative evaluation of CBL's pedagogical effectiveness and the use of CBL for teaching professional skills.