The reconfigurable intelligent surface (RIS) has aroused much research attention recently due to its potential benefits in 5G and beyond wireless networks. This paper considers a general multi-hop RIS-aided multi-user communication system and the weighted sum-rate maximization problem is studied by jointly designing the active beamforming matrix at the base station and multiple phase-shift matrices at the RISs (considering both continuous and discrete phase constraints). To tackle the resulting highly nonconvex optimization problem, a problem-tailored low-complexity and globally convergent algorithm based on block minorization-maximization (BMM) is proposed. The effectiveness of the proposed BMM approach and the performance improvement gained with multi-hop RISs are both demonstrated through numerical simulations. The merits of the proposed algorithms are further illustrated by indicating their adaptivity in solving many other RIS-related system designs.