The surge of interest in culturally aware and adapted Natural Language Processing (NLP) has inspired much recent research. However, the lack of common understanding of the concept of "culture" has made it difficult to evaluate progress in this emerging area. Drawing on prior research in NLP and related fields, we propose an extensive taxonomy of elements of culture that can provide a systematic framework for analyzing and understanding research progress. Using the taxonomy, we survey existing resources and models for culturally aware and adapted NLP, providing an overview of the state of the art and the research gaps that still need to be filled.