Recent efforts to understand aggregate student loan debt have shifted the focus away from undergraduate borrowing and toward dramatically rising debt among graduate and professional students. We suggest educational debt plays a key role in social stratification by either deterring bachelor's degree holders from disadvantaged and underrepresented backgrounds from pursuing lucrative careers through advanced degree programs or imposing a high cost for entry. We speculate that the ongoing personal financing of advanced degrees, changes to funding in higher education, and increasing returns to and demand for postbaccalaureate degrees have created a perfect storm for those seeking degrees beyond college. We find that aggregate increases in borrowing among advanced degree students between 1996 and 2016 can be explained in part by increasing enrollment rates, particularly among master's degree students, and large, secular increases in graduate and professional students' undergraduate and graduate borrowing. In contrast to undergraduate debt alone, the burden of educational debt among graduate borrowers appears to have fallen on students from lower socioeconomic backgrounds and historically underserved students of color more so than their more advantaged counterparts and on women more so than men. However, we also find that median advanced degree wage premia over those of bachelor's degree holders are substantial for many who graduate with advanced degrees but are particularly high for African American and low socioeconomic status graduates, complicating simple conclusions about the stratification of debt at the postgraduate level.