This paper presents a critical review of how different socio-technical design processes for AI-based systems, from scholarly works and industry, support the creation of value-sensitive AI (VSAI). The review contributes to the emerging field of human-centred AI, and the even more embryonic space of VSAI in four ways: (i) it introduces three criteria for the review of VSAI based on their contribution to design processes’ overall value-sensitivity, and as a response to criticisms that current interventions are lacking in these aspects: comprehensiveness, level of guidance offered, and methodological value-sensitivity, (ii) it provides a novel review of socio-technical design processes for AI-based systems, (iii) it assesses each process based on the mentioned criteria and synthesises the results into broader trends, and (iv) it offers a resulting set of recommendations for the design of VSAI. The objective of the paper is to help creators and followers of design processes—whether scholarly or industry-based—to understand the level of value-sensitivity offered by different socio-technical design processes and act accordingly based on their needs: to adopt or adapt existing processes or to create new ones.