Effective doctoral education in chemistry has been discussed at length for over a century and is tied to the health of the United States economy. In this literature review, 257 resources relating to doctoral education in chemistry spanning from 1909 to 2019 were collected for the purpose of providing a systematic review of the major issues facing doctoral education in chemistry. A total of eight themes were identified as major issues that were raised consistently throughout the past several decades, some for more than a century. In the current educational system, many researchers believe that doctoral students are (1) overly specialized in their training, (2) ill-prepared for nonacademic careers, (3) ill-prepared for teaching positions, and (4) potentially overproduced compared to genuine job opportunities. Additionally, (5) graduate programs in chemistry have not changed significantly for many decades, (6) single-project funding has greatly impacted the educational experience of doctoral students in both positive and negative ways, (7) the goals of doctoral education revolve around developing students' independent research ability, and (8) the majority of the literature regarding doctoral education is not based on empirical investigations. On one extreme, chemistry faculty and other key stakeholders may view the bleak outlook presented by the literature as a crisis demanding immediate and drastic reform. On the other extreme, they may view the criticisms raised as relatively minor areas of improvement to an otherwise effective system. Regardless of an individual's perspective of the severity of these identified issues, questions are provided that can catalyze discussion to encourage reflections on current practices in local chemistry doctoral programs.