In recent years, there has been a surge of interest in Cultural NLP, with substantial efforts to create globally inclusive NLP systems. The rapid growth of literature in this field makes it difficult to track trends in methods and data resources. To address this, we survey over 375 papers to answer three complementary questions: (1) What Cultural Capabilities (CCs) are being targeted in NLP systems? (2) How are cultural data resources being created? and (3) What methods are being used to improve the CCs of those systems? We discuss trends observed across the three questions, and identify relevant research gaps. To facilitate further research in this field, we release our full list of surveyed papers, in the form of an interactive web interface, CultureMine, which includes a feature to allow researchers to add their work; we hope this facilitates future research and proves to be a valuable resource for the Cultural NLP community.