Model merging conflicts occur when different stakeholders aim to integrate their contradicting changes that are applied concurrently to update software models. We conduct an extensive systematic mapping study on conflict management techniques and relevant collaboration attributes to the versioning and merging models from 2001 to the middle of 2021. This study follows the standard guidelines within the software engineering domain. We analyzed a total of 105 articles extracted from an initial pool of more than 1800 articles to infer a taxonomy for conflict management techniques. We use this taxonomy to classify existing approaches to understand characteristics, shortcomings, and challenges on conflict management techniques in merging models. It also provides a solid foundation for future work in this area. We show that syntactic conflicts are the most studied type and that the top three popular conflict detection techniques are constraint violation, change overlapping, and pattern matching. We observe the lack of a comprehensive state-of-the-art comparison between academic or industrial tools, as well as the need for real-world case studies. Finally, we show that recent trends have focused on online collaboration, where teams of stakeholders work on large-scale models.