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Reconfigurable intelligent surface (RIS)-aided near-field communications are investigated. First, the necessity of investigating RIS-aided near-field communications and the advantages brought about by the unique spherical wave-based near-field propagation are discussed. Then, the family of patch array-based RISs and metasurface-based RISs is introduced along with respective near-field channel models. A pair of fundamental performance limits of RIS-aided near-field communications, namely, their power scaling law and effective degrees of freedom (EDOF), are analyzed for both patch array-based and metasurface-based RISs, which reveals the potential performance gains that can be achieved. Furthermore, associated near-field beam training and beamforming design issues are studied, where a two-stage hierarchical beam training approach and a low-complexity element-wise beamforming design are …