We describe self-organizing network (SON) concepts and architectures and their potential to play a central role in 5G deployment and next-generation networks. Our focus is on the basic SON use case applied to radio access networks (RAN), which is self-optimization. We analyze SON applications’ rationale and operation, the design and dimensioning of SON systems, possible deficiencies and conflicts that occur through the parallel operation of functions, and describe the strong reliance on machine learning (ML) and artificial intelligence (AI). Moreover, we present and comment on very recent proposals for SON deployment in 5G networks. Typical examples include the binding of SON systems with techniques such as Network Function Virtualization (NFV), Cloud RAN (C-RAN), Ultra-Reliable Low Latency Communications (URLLC), massive Machine-Type Communication (mMTC) for IoT, and automated backhauling, which lead the way towards the adoption of SON techniques in Beyond 5G (B5G) networks.