Scholarly knowledge graphs (SKG) are knowledge graphs representing research-related information, powering discovery and statistics about research impact and trends. Author name disambiguation (AND) is required to produce high-quality SKGs, as a disambiguated set of authors is fundamental to ensure a coherent view of researchers’ activity. Various issues, such as homonymy, scarcity of contextual information, and cardinality of the SKG, make simple name string matching insufficient or computationally complex. Many AND deep learning methods have been developed, and interesting surveys exist in the literature, comparing the approaches in terms of techniques, complexity, performance, etc. However, none of them specifically addresses AND methods in the context of SKGs, where the entity-relationship structure can be exploited. In this paper, we discuss recent graph-based methods for AND, define a framework through which such methods can be confronted, and catalog the most popular datasets and benchmarks used to test such methods. Finally, we outline possible directions for future work on this topic.