This article surveys the state of the art in spectrum prediction and learning, summarizes applications, techniques, main metrics, computational complexity, and provides practical examples. We focus on a cellular case study and define required improvements to database-assisted spectrum sharing. The use of history information and predictive spectrum modeling at different time scales provides valuable information to regulators, operators, and users of dynamic spectrum access networks. Prediction enables dynamic spectrum sharing systems to operate proactively, and consequently improves the performance in terms of reducing delays and interference among coexisting systems. Current database-assisted spectrum sharing concepts are in fact too static for many applications. Our numerical results on local-aware predictive spectrum allocation show the advantage of predictive operation in a vehicle-to-everything (V2X) scenario.