With the availability of petabytes of oceanographic observations and numerical model simulations, artificial intelligence (AI) tools are being increasingly leveraged in a variety of applications. In this paper, these applications are reviewed from the perspectives of identifying, forecasting, and parameterizing ocean phenomena. Specifically, the usage of AI algorithms for the identification of mesoscale eddies, internal waves, oil spills, sea ice, and marine algae are discussed in this paper. Additionally, AI-based forecasting of surface waves, the El Niño Southern Oscillation, and storm surges is discussed. This is followed by a discussion on the usage of these schemes to parameterize oceanic turbulence and atmospheric moist physics. Moreover, physics-informed deep learning and neural networks are discussed within an oceanographic context, and further applications with ocean digital twins and physics-constrained AI algorithms are described. This review is meant to introduce beginners and experts in the marine sciences to AI methodologies and stimulate future research toward the usage of causality-adherent physics-informed neural networks and Fourier neural networks in oceanography.