There are widespread policy concerns to improve (widen and increase) science, technology, engineering, and mathematics participation, which remains stratified by ethnicity, gender, and social class. Despite being interested in and highly valuing science, Black students tend to express limited aspirations to careers in science and remain underrepresented in post-16 science courses and careers, a pattern which is not solely explained by attainment. This paper draws on survey data from nationally representative student cohorts and longitudinal interview data collected over 4 years from 10 Black African/Caribbean students and their parents, who were tracked from age 10-14 (Y6-Y9), as part of a larger study on children's science and career aspirations. The paper uses an intersectional analysis of the qualitative data to examine why science careers are less "thinkable" for Black students. A case study is also presented of two young Black women who "bucked the trend" and aspired to science careers. The paper concludes with implications for science education policy and practice.