k-way graph partitioning is an NP-complete problem, which is applied to various tasks such as route planning, image segmentation, community detection, and high-performance computing. The approximate methods constitute a useful solution for these types of problems. Thus, many research studies have focused on developing meta-heuristic algorithms to tackle the graph partitioning problem. Local search is one of the earliest methods that has been applied efficiently to this type of problem. Recent studies have explored various types of local search methods and have improved them such that they can be used with the partitioning process. Moreover, local search methods are widely integrated with population-based approaches, to provide the best diversification and intensification for the problem space. This study emphasizes the local search approaches, as well as their combination with other graph partitioning approaches. At present, none of the surveys in the literature has focused on this class of state of the art approaches in much detail. In this study, the vital parts of these approaches including neighborhood structure, acceptance criterion, and the ways of combining them with other approaches, are highlighted. Additionally, we provide an experimental comparison that shows the variance in the performance of the reviewed methods. Hence, this study clarifies these methods to show their advantages and limitations for the targeted problem, and thus can aid in the direction of research flow towards the area of graph partitioning. © 2019 Fuji Technology Press. All rights reserved.