Animal behavior serves as a reliable indicator of the adaptation of organisms to their environment and their overall well-being. Through rigorous observation of animal actions and interactions, researchers and observers can glean valuable insights into diverse facets of their lives, encompassing health, social dynamics, ecological relationships, and neuroethological dimensions. Although state-of-the-art deep learning models have demonstrated remarkable accuracy in classifying various forms of animal data, their adoption in animal behavior studies remains limited. This survey article endeavors to comprehensively explore deep learning architectures and strategies applied to the identification of animal behavior, spanning auditory, visual, and audiovisual methodologies. Furthermore, the manuscript scrutinizes extant animal behavior datasets, offering a detailed examination of the principal challenges confronting this research domain. The article culminates in a comprehensive discussion of key research directions within deep learning that hold potential for advancing the field of animal behavior studies.