This report is deliverable D5.2 (T5.2 and T5.3) of the Horizon Europe project ''Global Strategy for Skills, Migration and Development'' (GS4S). In a context of shared high priority given to structural skill shortages, there is a wide consensus at Member State and EU level that international migrants and refugees who are already legally in the continent represent an under-used and potentially valuable pool of human resources. But the way in which this priority is interpreted and acted upon varies deeply across countries. Some policies and programmes to promote the up-skilling and re-skilling of migrant and refugee workers (and inactive people with migration background) exist in all Member States, but with different design and levels of uptake. It is however clear, that the impact of existing up-/re-skilling schemes is largely insufficient to "make the most of migrants' skills". The goal of this report is to go beyond the generic complaint through a more articulate empirical understanding of this untapped labour potential. Based on qualitative and participatory research conducted in four Member States (Estonia, Germany, Italy, the Netherlands) and in Switzerland, we analyse the main hurdles (at both personal and structural level) and the main mechanisms preventing a more systematic and effective involvement of migrants and refugees in up-/re-skilling initiatives. In doing so, we show that these obstacles are linked to broader socio-economic and legal conditions that shape the opportunities available to migrants and refugees. This combination creates what has been called the "hyper-precarity trap" (Lewis et al., 2014; Schenner et al., 2019; Palalar Alkan et al., 2024), describing how the interaction between limited rights, restricted access to services, and insecure or unstable jobs can push people into multiple forms of insecurity at the same time, making it difficult for them to improve their situation. On this basis, we highlight some policy implications and potential avenues for policy innovation.