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Purpose This purpose of this study is to provide an overview of the current state of research on Lean Six Sigma (LSS) and Industry 4.0 and the key aspects of the relationships between them. The research analyses LSS's evolution and discusses the future role of LSS 4.0 in an increasingly digitalized world. We present the benefits and motivations of integrating LSS and Industry 4.0 as well as the critical success factors and challenges within this emerging area of research. Design/methodology/approach A systematic literature review methodology was established to identify, select and evaluate published research. Findings There is a synergistic nature between LSS and Industry 4.0. Companies having a strong LSS culture can ease the transition to Industry 4.0 while Industry 4.0 technologies can provide superior performance for companies who are using LSS methodology. Research limitations/implications One limitation of this research was that as this area is a nascent area, the researchers were limited in their literature review and research. A more comprehensive longitudinal study would yield more data. There is an opportunity for further study and analysis. Practical implications This study reviews the evolution of LSS and its integration with Industry 4.0. Organisations can use this study to understand the benefits and motivating factors for integrating LSS and Industry 4.0, the Critical Success Factors and challenges to such integration. Originality/value This is the first systematic literature review on LSS 4.0 and can provide insight for practitioners, organisations and future research directions.