Teaching undergraduate students to read primary scientific literature (PSL) is cited as an important goal for many science, technology, engineering, and math (STEM) classes, given a range of cognitive and affective benefits for students who read PSL. Consequently, there are a number of approaches and curricular interventions published in the STEM education literature on how to teach students to read PSL. These approaches vary widely in their instructional methods, target student demographic, required class time, and level of assessment demonstrating the method's efficacy. In this Essay, we conduct a systematic search to compile these approaches in an easily accessible manner for instructors, using a framework to sort the identified approaches by target level, time required, assessment population, and more. We also provide a brief review of the literature surrounding the reading of PSL in undergraduate STEM classrooms and conclude with some general recommendations for both instructors and education researchers on future areas of investigation.