The study of innovation in non-human animals (henceforth: animals) has recently gained momentum across fields including primatology, animal behaviour and cultural evolution. Examining the rate of innovations, and the cognitive mechanisms driving these innovations across species, can provide insights into the evolution of human culture. Especially relevant to the study of human culture is one of our closest living relatives, the chimpanzee (Pan troglodytes). Both wild and captive chimpanzees demonstrate an impressive ability to innovate solutions to novel problems, but also a striking level of conservatism in some contexts, creating a unique and at times puzzling, picture of animal innovation. Whilst the animal innovation field is rife with potential for expanding our knowledge of human and non-human cognition and problem-solving, it is undermined by a lack of consistency across studies. The field is yet to settle on a definition of the term 'innovation', leading to studies being incomparable across and even within the same species. Here, we fill two gaps in the literature. First, we discuss some of the most prevalent definitions of 'innovation' from different fields, highlighting similarities and differences between them. Secondly, we provide an up-to-date review of accounts of innovations in both wild and captive chimpanzees. We hope this review will provide a resource for researchers interested in the study of innovation in chimpanzees and other animals, as well as emphasising the need for consistency in the way in which innovations are reported.