Many technology designers strive to involve end users in the design process, aiming to produce better outcomes. However, designers may struggle to engage autistic users effectively due to a lack of understanding of autistic characteristics and preferences. This systematic literature review aimed to identify how autistic adolescents and adults can best be engaged in effective participatory design activities. Seven databases were searched for articles reporting technology design involving autistic people, returning 276 results. Using the PRISMA approach, 258 were excluded due to not meeting the inclusion criteria. The remaining 18 articles were then quality assessed. A thematic analysis revealed five core themes: (1) Engagement: the importance of investment in, and ownership of, the design process to create engagement; (2) Relationships: building relationships through collaboration and careful facilitation; (3) Skills development: the development of personal skills such as teamwork, design and self-advocacy in order to grow confidence; (4) Structure: providing context and structure to make the design experience feel safe and predictable; and (5) Support: the importance of support and consideration of individual needs as well as discouraging negative behaviours. Valuing participants as equal partners in design emerged as an, arguably, universal principle. The specific needs and preferences of autistic people must be understood and respected by designers. This goes beyond obvious accommodations such as providing a quiet and safe environment, and requires a deeper, more personal engagement with the individuals and their interests. We provide tangible recommendations for increasing engagement and aiding the design process.