This study reviews literature on racially equitable admissions practices relevant to graduate programs in STEM. Graduate Record Exam (GRE) scores correlate more strongly with race, gender, and socioeconomic status than performance metrics for research during or after graduate school. Structural changes to admissions processes that can improve equity of admissions decisions and reduce correlations between admissions decisions and demographic data include using holistic review or composite scores that quantize more components of an application, removing hard limits on course requirements, admitting students as a cohort instead of to individual faculty sponsors, and diversifying admissions committees. Some alternative scoring methods attempt to measure personality traits, but performing these measurements during admissions may present difficulties. Bridge programs--whether they are implemented as collaborations with a minority-serving institution, a personalized educational program for each student admitted to a program, or a stand-alone program before the doctoral degree program--may be able to improve both recruitment and retention of students with underrepresented racial and ethnic identities in their field of study. Finally, financial barriers to applications can disproportionately affect underrepresented applicants due to systemic racism. We end with recommendations for graduate programs to improve equity in admissions processes.