The concept of social structure, present in social ontology since the 19th century, has been used in various, not always clearly specified, meanings. The present use of the concept has been decisively influenced by the elaborations in the hands of the so-called “new structuralists” of the 1970s: Pierre Bourdieu, Roy Bhaskar and Anthony Giddens. To understand the contemporary developments, it is necessary to be acquainted with its formative influences. In the paper, we compare the approaches of Bhaskar and Giddens, especially in the context of their mutual compatibility and the challenges facing anyone wanting to develop their own concept of social structure based on the elaborations of the concept by Bhaskar and Giddens. The most fundamental issues appear to be especially the mode of existence of social structures, the heterogeneous character of different kinds of social structures, and the transition from the ontology of the natural world to that of the social world by Bhaskar.