Assembly lines are mass production systems which are significant in the industrial production of both standard and customised products. Currently, industrial companies offer several products and it is common for an assembly system to have multiple assembly lines. Parallel assembly lines are multiple lines located in such a way as to allow improvements in the system’s efficiency through the use of common resources. In recent years several research studies have been made on parallel assembly lines. In this paper, we survey the parallel assembly lines balancing problem (PALBP) studies. Moreover, a classification scheme is provided to ease understanding. Finally, the main gaps in the literature are described and future research directions are presented.