Many cultural phenomena cannot be understood by studying traits in isolation. Instead, they are embedded in webs of relations, layered with rich social meaning, and sequentially acquired and evaluated, \emph{filtered}, in light of previously acquired traits. Incorporating multiple traits and their relations is needed to understand the organization, dynamics, and emergent products of cultural evolution. We argue that a systems approach offers the potential for: (i) a more thorough understanding of the source and character of emergent phenomena, crucial for understanding the origin and historical development of culture; (ii) an increased scope of cultural evolution, whereby faithful transmission, self-organization and filtering of culture can be accounted for by systems dynamics without the need for strong assumptions about innate machinery; and (iii) a more robust theoretical connection between cultural evolution and processes of development as they are studied in developmental psychology and related fields.