Abstract: In this contribution, we present a survey on the radio resource allocation techniques in orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA) systems. This problem goes back to 1960s and that is related to properly and efficiently allocate the radio resources, namely subcarriers and power. We start by overviewing the main open issues in OFDM. Then, we describe the problem formulation in OFDMA, and we review the existing solutions to allocate the radio resources. The goal is to discuss the fundamental concepts and relevant features of different radio resource management criteria, including water-filling, max–min fairness, proportional fairness, cross-layer optimization, utility maximization, and game theory, also including a toy example with two terminals to compare the performance of the different schemes. We conclude the survey with a review of the state-of-the-art in resource allocation for next-generation wireless networks, including multicellular systems, cognitive radio, and relay-assisted communications, and we summarize advantages and common problems of the existing solutions available in the literature. The distinguishing feature of this contribution is a tutorial-style introduction to the fundamental problems in this area of research, intended for beginners on this topic.