Quantum computing and artificial intelligence are two highly topical fields of research that can benefit from each other’s discoveries by opening a completely new scenario in computation, that of quantum artificial intelligence. Indeed, on the one hand, artificial intelligence algorithms can be made computationally more efficient due to the potential speedup enabled by quantum phenomena; on the other hand, the complex development of quantum computing technologies and methodologies can be properly supported by the use of classical artificial intelligence approaches. The “entanglement” of these two disciplines is opening up completely new directions in computer science research, and this survey aims to provide a systematic and taxonomic overview of the work that has already been done and that which will begin in the near future.