ABSTRACT Due to the high cost pressure and the increasing variant diversity, the cooperation of humans and robots represents a promising technological solution to achieve higher flexibility and efficiency in assembly. It is therefore attracting significant interest from both researchers and practitioners. As a result, numerous reviews have been published addressing different aspects of human-robot collaboration, such as safety, interaction modalities, programming, and applications. However, in this paper, for the first time, the aspect of task allocation for collaborative assembly is methodologically examined through a systematic literature review. This paper presents the current state of the art in task allocation approaches, investigates the criteria for deciding on a suitable task assignment, and discusses challenges and future research needs. After filtering the 521 publications that resulted from the initial search process, 37 relevant publications were included in the analysis and grouped into a proposed classification consisting of two main categories, static and dynamic task allocation approaches. Based on the results of the literature review, this paper presents a reference model for human-robot collaborative assembly.