This chapter is about the access to networks with valuable resources (social capital) of individuals with a migrant background. Findings from the empirical studies in this field that I have conducted in Sweden over the last 20 years are the main basis for my arguments here: (i) it is not an individual’s social networks per se but the resources embedded in these social networks which define a person’s social capital; (ii) immigrants have different social and economic backgrounds and positions. An intersectional perspective challenges studies on the social capital of immigrants that lump all immigrants together as one homogenous group; (iii) social capital is a significant device for reproducing the existing hierarchical structure of society and the distinct power positions of various social groups; (iv) although the stratification effect of social capital is the predominant pattern, some groups or individuals from the unprivileged strata of society and other low-status people (like immigrants) have been able to gain access to resources beyond their immediate social networks, through institutional mediation or via membership in civil-society organisations (the “counter stratification” effect of social capital); finally (iv) the outcomes of social capital may differ due to context specificity.