The food industry is an important sector of the world economy, that faces many challenges providing a wide range of products with short delivery times and at low-cost. Continuous Improvement (CI) initiatives could assist this industry manage its challenges as the global market endures economic and political crises. Lean and Six Sigma are two widely used and recognized CI initiatives and are often hybridized as Lean Six Sigma. However, it is not clear how appropriate these strategies are for the food industry. A systematic literature review was performed to identify the appropriateness of Lean, Six Sigma and Lean Six Sigma initiatives (L&SSi) for improvement in the food industry. The aim is to consolidate the existing knowledge about the application of L&SSi in the food industry, analyze the L&SSi evolution within the sector and identify the relevant aspects of implementation such as drivers of adoption, critical success factors, tools and methods applied, barriers faced and benefits obtained. The review suggests that L&SSi are effective in the food industry context. Their implementation in the sector is still growing. Their use was found to reduce costs and increase productivity. Human factors and the food industry characteristics were identified as the main barriers to implementing these initiatives. Future research to investigate the degree that L&SSi practices were adopted in the food industry and to identify the best practices to implement these initiatives is suggested. •Food industry adopts Lean & Six Sigma initiatives mainly to increase productivity and to reduce costs and inventory.•There is a great opportunity for Food Industry to improve their performance by implementing Lean & Six Sigma initiatives.•The food industry characteristics and human factors impact the adoption of some Lean & Six Sigma tools and methods.