As global demand for minerals in general, and critical minerals in particular, intensifies, discovering new deposits has become a pressing scientific challenge. This task requires integrating heterogeneous geoscientific data, including geophysical, geochemical, remote sensing, geological, and textual sources, across vast underexplored terrains. Such integration poses distinct challenges for Machine Learning (ML), including extreme label scarcity in a natural Positive-Unlabeled setting, spatial non-stationarity that violates independent and identically distributed (i.i.d.) assumptions, and multi-format data heterogeneity. Despite this growing body of work, a unified review connecting classical ML, deep learning, and foundation models across the full exploration pipeline is lacking. This survey reviews ML and foundation models across the mineral exploration pipeline.We cover domain-specific ML for geological, geophysical, geochemical, and remote sensing tasks; mineral prospectivity mapping (MPM) from classical methods through deep learning and 3D prediction; foundation models and NLP-based knowledge extraction across multiple geoscience modalities; and the supporting ecosystem of open datasets, portals, and software. For each area, we assess the current maturity of foundation model applications, identify domain-specific adaptations required, and highlight open gaps where AI research could have significant impact, particularly multi-modal foundation models, cross-region transfer learning, uncertainty-aware prediction, and AI agents for exploration decision support. A curated list of resources is available on the project page.