As postdoctoral training has become a requirement in many STEMM fields the influence of postdoc hiring on STEMM labor force inclusion and diversity has increased, yet postdoc hiring processes have received only limited attention from researchers. Drawing on status theory and data for 769 postdoctoral recruitments, we systematically analyze the relationship between gender, race-ethnicity, and postdoctoral hiring. The findings show: (1) differences by gender and race-ethnicity in application rates, and in whether an applicant is seriously considered, interviewed, and offered the postdoc position; (2) hiring disparities correlate with between-group differences in applicants' network connections, referrer prestige, and academic human capital; (3) between-group differences in network connections have the greatest power to account for hiring disparities; and (4) hiring processes may differ by applicant gender or race-ethnicity, the female representation in the STEMM field and the race of the search committee chair. We discuss competing interpretations of the results and highlight directions for future research.