Computer-based learning technologies are now being used worldwide, but are mostly researched in a small number of countries and contexts. Increasing research suggests that modifications are needed to make computer-based learning responsive for all students worldwide. In this article for the inaugural special issue of Computer-Based Learning in Context, we discuss the virtues and limitations of existing theoretical paradigms of culture and context, relevant to computer-based learning. We note cases where existing approaches are successful, while listing some key phenomena in computer-based learning that fail to be explained by current approaches. We close by unpacking some open questions that limit our ability to make progress on such systems and suggesting some of the attributes of useful next-generation theory on culture and context in computer-based learning. In particular, we discuss possible steps forward that can be used to better operationalize culture and make theory on culture and context more concrete and actionable. [This paper was published in "Computer-Based Learning in Context" v1 n1 p1-13 2019.]