This paper is a tutorial introduction to the field of unsourced multiple access (UMAC) protocols. We first provide a historical survey of the evolution of random access protocols, focusing specifically on the case in which uncoordinated users share a wireless broadcasting medium. Next, we highlight the change of perspective originated by the UMAC model, in which the physical and medium access layer's protocols cooperate, thus reframing random access as a novel coding-theoretic problem. By now, a large variety of UMAC protocols (codes) emerged, necessitating a certain classification that we indeed propose here. Although some random access schemes require a radical change of the physical layer, others can be implemented with minimal changes to existing industry standards. As an example, we discuss a simple modification to the 5GNR Release 16 random access channel that builds on the UMAC theory and that dramatically improves energy efficiency for systems with even moderate number of simultaneous users (e.g., $5-10$ dB gain for $10-50$ users), and also enables handling of high number of users, something completely out of reach of the state-of-the-art.

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