Ocean is a highly complex and nonlinear dynamical system. The inevitable errors in both data and numerical models lead to uncertainties in ocean numerical prediction. By understanding features and properties in the ocean on multiple scales, it is important to quantify and estimate the predictability of the ocean, and analyze the reasons and mechanism of error growth. The efforts focus on investigating the method to reduce the uncertainties and errors in forecasting and increase the time limit of ocean predictability. The advances will result in improved marine forecasting models and forecasting skill. Understanding limitations and identifying the research needed to increase accuracy will lead to fundamental progress in ocean forecast, which is of great significance. The present study described and illustrated the mechanics and computations involved in modeling and predicting uncertainties for ocean prediction and its modern applications. Firstly, it discussed the fundamental concept and classification of the ocean predictability. The research status of ocean predictability is introduced including the dynamics methodologies and the ocean ensemble prediction. Three of the dynamical computational methodologies including the singular vector, Lyapunov exponent and bred vector method were introduced. Three ocean ensemble prediction methods including initial condition ensemble, multi-model ensemble and atmospheric forcing ensemble were described and illustrated. Finally, this paper gave a future prospective of ocean predictability and its application.