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The residential sector is currently one of the major contributors to the global energy balance. However, the energy demand of residential users has been so far largely uncontrollable and inelastic with respect to the power grid conditions. With the massive introduction of renewable energy sources and the large variations in energy flows, also the residential sector is required to provide some flexibility in energy use so as to contribute to the stability and efficiency of the electric system. To address this issue, demand management mechanisms can be used to optimally manage the energy resources of customers and their energy demand profiles. A very promising technique is represented by demand-side management (DSM), which consists in a proactive method aimed at making users energy-efficient in the long term. In this paper, we survey the most relevant studies on optimization methods for DSM of residential consumers. Specifically, we review the related literature according to three axes defining contrasting characteristics of the schemes proposed: DSM for individual users versus DSM for cooperative consumers, deterministic DSM versus stochastic DSM and day-ahead DSM versus real-time DSM. Based on this classification, we provide a big picture of the key features of different approaches and techniques and discuss future research directions.