Automated bioacoustics classification has received increasing attention from the research community in recent years due its cross-disciplinary nature and its diverse application. Applications in bioacoustics classification range from smart acoustic sensor networks that investigate the effects of acoustic vocalizations on species to context-aware edge devices that anticipate changes in their environment adapt their sensing and processing accordingly. The research described here is an in-depth survey of the current state of bioacoustics classification and monitoring. The survey examines bioacoustics classification alongside general acoustics to provide a representative picture of the research landscape. The survey reviewed 124 studies spanning eight years of research. The survey identifies the key application areas in bioacoustics research and the techniques used in audio transformation and feature extraction. The survey also examines the classification algorithms used in bioacoustics systems. Lastly, the survey examines current challenges, possible opportunities, and future directions in bioacoustics.