Purpose This study aims to discover, compare and analyse the primary works that integrate Lean Six Sigma (LSS) and discrete event simulation (DES), exploring theoretical aspects to provide support for future integrated applications of the methods. Design/methodology/approach The authors carried out a systematic literature review involving selecting and evaluating papers in six scientific databases. This approach aimed to explore various aspects related to the integration of LSS and DES. Among the main aspects evaluated, the authors highlight the primary steps that involve applying both techniques, the structural organisation of each method, the associated objectives, adopted software, application areas, frameworks and other pertinent factors. Findings LSS offers DES a problem-solving-oriented approach, while DES allows LSS to test various scenarios planned for the DMAIC improvement phase. Despite being a promising theme, few studies examine these methods in an integrated manner. Moreover, among the works analysed, none presents a framework with guidelines for implementing these methods in an integrated way. Research limitations/implications This paper may not have included some of the studies due to the inaccessibility and selection criteria followed for the study. Originality/value This paper offers an overview and research insights considering the state of the art on integrating LSS and DES methods for researchers and practitioners in continuous improvement and computer simulation areas.