Nowadays, automotive and aerospace are seeking lightweight designs to improve fuel efficiency and reduce cost. Topology optimization (TO) is an efficient numerical tool for optimizing material distributions based on a given problem statement. The first landmark of TO is single material topology optimization (SMTO), which employs only one candidate material for TO. Owing to its robustness and ease of implementation, SMTO serves as the foundation of TO methodologies. A notable evolution of SMTO is multi-material topology optimization (MMTO), which optimizes the distribution of multiple candidate materials simultaneously. Due to improved design freedom, MMTO generally yields superior designs than those obtained by SMTO. However, the main limitation of MMTO lies in the assumption that dissimilar materials are perfectly bonded together, which reduces the manufacturability of the TO solutions. To address this issue, multi-material and multi-joint topology optimization (MM-MJ-TO) is proposed, in which the material properties of joints connecting dissimilar structural materials are explicitly modeled. Compared with MMTO, MM-MJ-TO yields more practical and manufacturable TO solutions, making it a key milestone in the development of TO. This paper presents a comprehensive review of density-based MM-MJ-TO works, covering key aspects including optimization schemes, interface detection and joint modelling. In addition, future research directions of MM-MJ-TO are discussed, highlighting potential approaches to further enhance its practical applicability.