The reconfigurable intelligent surface (RIS) has arose an upsurging research interest recently due to its promising outlook in 5G-and-beyond wireless networks. With the assistance of RIS, the wireless propagation environment is no longer static and could be customized to support diverse service requirements. In this paper, we will approach the rate maximization problems in RIS-aided wireless networks by considering the beamforming and reflecting design jointly. Three representative design problems from different system settings are investigated based on a proposed unified algorithmic framework via the block minorization-maximization (BMM) method. Extensions and generalizations of the proposed framework in dealing with some other related problems are further presented. Merits of the proposed algorithms are demonstrated through numerical simulations in comparison with the state-of-the-art methods.