Many autistic people are unemployed. Of those who are employed, many are in roles that do not reflect their skills, qualifications and/or capabilities, and little is known about how autistic people progress throughout their careers. This study aimed to review and synthesise the existing evidence about career progression for autistic people. In total, 33 studies met the criteria for inclusion, though no study directly aimed to explore the topic. Our findings suggest that underemployment is common within the autistic population. Indirectly, we identified several potential barriers and facilitators of career progression for autistic people. Possible barriers included personal (e.g. gaps in education and employment history), relational (e.g. disclosing an autism diagnosis) and organisational factors (e.g. inadequate employment support). Adequate employment support was the most frequently discussed facilitator. Future research should seek to identify the most successful employment supports for autistic people over the long term to ensure that all autistic people are able to live -- and work -- in ways that are meaningful to them.