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Artificial intelligence and machine learning are accelerating research in Earth system science, with huge potential for impact and challenges in ocean prediction. Such algorithms are being deployed on different aspects of the forecasting workflow with the aim of improving its speed and skill. They include pattern classification and anomaly detection; regression and diagnostics; and state prediction from nowcasting to synoptic, sub-seasonal, and seasonal forecasting. This brief review emphasizes scientific machine learning methods that have the capacity to embed domain knowledge; to ensure interpretability through causal explanation, to be robust and reliable; to involve effectively high-dimensional statistical methods, supporting multi-scale and multi-physics simulations aimed at improving parameterization; and to drive intelligent automation, as well as decision support. An overview of recent numerical developments is discussed, highlighting the importance of fully data-driven ocean models for future expansion of ocean forecasting capabilities.