The rise of machine learning (ML) has significantly advanced the field of coastal oceanography. This review aims to examine the existing deficiencies in numerical predictions of storm surges and the effort that has been made to improve the predictive accuracy through the application of ML. The readers are guided through the steps required to implement ML algorithms, from the first step of formulating problems to data collection and determination of input features to model selection, development and evaluation. Additionally, the review explores the application of hybrid methods, which combine the bilateral advantages of data-driven methods and physics-based models. Furthermore, the strengths and limitations of ML methods in predicting storm surges are thoroughly discussed, and research gaps are identified. Finally, we outline a vision toward a trustworthy and reliable storm surge forecasting system by introducing novel physics-informed ML techniques. We are meant to provide a primer for beginners and experts in coastal ocean sciences who share a keen interest in ML methodologies in the context of storm surge problems.