Knowing metastasis is the primary cause of cancer-related deaths, incentivized research directed towards unraveling the complex cellular processes that drive the metastasis. Advancement in technology and specifically the advent of high-throughput sequencing provides knowledge of such processes. This knowledge led to the development of therapeutic and clinical applications, and is now being used to predict the onset of metastasis to improve diagnostics and disease therapies. In this regard, predicting metastasis onset has also been explored using artificial intelligence approaches that are machine learning, and more recently, deep learning-based. This review summarizes the different machine learning and deep learning-based metastasis prediction methods developed to date. We also detail the different types of molecular data used to build the models and the critical signatures derived from the different methods. We further highlight the challenges associated with using machine learning and deep learning methods, and provide suggestions to improve the predictive performance of such methods.