We summarize national-scale data for Ph.D. earners in engineering or computer science from 2015 to 2019 whose post-graduate school employment is known, highlighting outcomes for biological/biomedical/biosystems engineering students. We use NSF's Survey of Earned Doctorates (SED), which has collected information from Ph.D. recipients in the USA since 1957. The data are collected at the time of degree completion and constitute a greater than 90% response rate. Compared to all engineering and computer science disciplines, biological/biomedical/biosystems engineering has a higher proportion going to 4yr/med/research institutions (52% vs. 33%) and non-profit (3.6% vs. 2.9%) and lower proportion going to industry (33% vs. 48%), government (4.3% vs. 8.4%), and is similar for non-US positions (6.1% vs. 5.7%). Compared to 2010--2014 biological/biomedical/biosystems engineering Ph.D. recipients, more 2015--2019 recipients are going to industry (25% to 33%) and fewer to 4yr/med/research institutions (59% to 52%) and government (5.3% to 4.3%). Across all engineering and computer science disciplines, a smaller proportion of females entered industry (43%) compared to males (49%), while a larger proportion of females entered 4yr/med/research institutions (37%) compared to males (32%). Over half of Asian doctoral recipients entered industry, as compared to 38% of Hispanic doctoral recipients. In contrast, a higher proportion of Hispanic individuals (37%) entered 4yr/med/research institutions after their doctoral programs, as compared to 31% of Asian doctoral recipients. Black doctoral recipients had the highest proportion enter positions in government (14%) and non-profit (4%) sectors. Our results are situated in the broader literature focused on postdoctoral career, training, and employment sectors and trends in STEM. We discuss implications for graduate programs, policymakers, and researchers.