Due to the recent proliferation of AI-enabled technology (AIET), the concept of anthropomorphism, human likeness in technology, has increasingly attracted researchers' attention. Researchers have examined how anthropomorphism influences users' perception, adoption, and continued use of AIET. However, researchers have yet to agree on how to conceptualize and operationalize anthropomorphism in AIET, which has resulted in inconsistent findings. A comprehensive understanding is thus needed of the current state of research on anthropomorphism in AIET contexts. To conduct an in-depth analysis of the literature on anthropomorphism, we reviewed 35 empirical studies focusing on conceptualizing and operationalizing AIET anthropomorphism, and its antecedents and consequences. Based on our analysis, we discuss potential research gaps and offer directions for future research.