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Future generation cellular networks are expected to provide ubiquitous broadband access to a continuously growing number of mobile users. In this context, LTE systems represent an important milestone towards the so called 4G cellular networks. A key feature of LTE is the adoption of advanced Radio Resource Management procedures in order to increase the system performance up to the Shannon limit. Packet scheduling mechanisms, in particular, play a fundamental role, because they are responsible for choosing, with fine time and frequency resolutions, how to distribute radio resources among different stations, taking into account channel condition and QoS requirements. This goal should be accomplished by providing, at the same time, an optimal trade-off between spectral efficiency and fairness. In this context, this paper provides an overview on the key issues that arise in the design of a resource allocation algorithm for LTE networks. It is intended for a wide range of readers as it covers the topic from basics to advanced aspects. The downlink channel under frequency division duplex configuration is considered as object of our study, but most of the considerations are valid for other configurations as well. Moreover, a survey on the most recent techniques is reported, including a classification of the different approaches presented in literature. Performance comparisons of the most well-known schemes, with particular focus on QoS provisioning capabilities, are also provided for complementing the described concepts. Thus, this survey would be useful for readers interested in learning the basic concepts before going into the details of a particular scheduling strategy, as well as for researchers aiming at deepening more specific aspects.