User-centric radio access technology (RAT) selection is a key communication paradigm, given the increased number of available RATs and increased cognitive capabilities at the user end. When considered against traditional network-centric approaches, user-centric RAT selection results in reduced network-side management load, and leads to lower operational costs for RATs, as well as improved quality of service (QoS) and quality of experience (QoE) for users. The complex between-users interactions involved in RAT selection require, however, specific analyses, toward developing reliable and efficient schemes. Two theoretical frameworks are most often applied to user-centric RAT selection analysis, i.e., game theory (GT) and multi-agent learning (MAL). As a consequence, several GT models and MAL algorithms have been recently proposed to solve the problem at hand. A comprehensive discussion of such models and algorithms is, however, currently missing. Moreover, novel issues introduced by next-generation communication systems also need to be addressed. This paper proposes to fill the above gaps by providing a unified reference for both ongoing research and future research directions in the field. In particular, the review addresses the most common GT and MAL models and algorithms, and scenario settings adopted in user-centric RAT selection in terms of utility function and network topology. Regarding GT, the review focuses on non-cooperative models, because of their widespread use in RAT selection; as for MAL, a large number of algorithms are described, ranging from game-theoretic to reinforcement learning (RL) schemes, and also including most recent approaches, such as deep RL (DRL) and multi-armed bandit (MAB). Models and algorithms are analyzed by comparatively reviewing relevant literature. Finally, open challenges are discussed, in light of ongoing research and standardization activities.