Assembly-line balancing is a significant issue in production systems. Employing industrial robots as the main production resource was a milestone in developing assembly lines, and emerging Industry 4.0 led industries to build collaborative assembly lines by combining robots and human operator skills. Recently, the majority of research on assembly line balancing has contributed to addressing aspects of utilizing robots in assembly lines and how they can increase line performance. Various models and methods are developed, considering different objectives and performance indicators. Despite the increasing number of studies in this area, a thorough literature review is lacking in identifying gaps, shedding light on research directions, and facilitating future development. This study systematically reviews assembly-line balancing studies targeted at assembly lines with industrial and collaborative robots. Studies are classified based on their objectives and reviewed for their solution method, line layout, and other essential specifications. A descriptive analysis is provided to assist researchers and practitioners in linking different properties of assembly lines to the objectives and applied methodologies. The results show that most studies developed models and solution methods that focused on simultaneously optimizing more than one objective. The review reveals that minimizing the cycle time is the most popular objective, and meta-heuristic algorithms are the dominant solution approaches. It is also observed that balancing assembly lines with collaborative robots has received more attention in the last five years with the emergence of Industry 4.0. The review also highlights gaps in the related literature and provides promising insights for future research.