Purpose This paper aims to present a review of literature that considers the use of quality frameworks in higher education (HE). Quality frameworks provide a minimum standard of teaching and learning of students. This systematic literature review identifies the tools and techniques to continuously improve the systems and processes that underpin teaching and learning are missing. With this in mind, the authors present a focus on Lean Six Sigma (LSS) as an improvement methodology adopted by the HE sector and present the factors that drive or hinder the implementation of LSS in higher education institutions (HEIs). Design/methodology/approach A review of the literature and thematic analysis has been undertaken relating to the application of quality frameworks and methodologies within the literature set. Findings The findings show that quality frameworks to be lacking insofar as their focus on compliance is no incentive for continuous improvement. This finding is not unique to the HEI sector and similar challenges exist in other sectors. A further finding identifies the need for academic professional practice to go beyond quality assurance to attend to the transformation of students. Together these present an apparent disconnect between continuous improvement methodology and HE quality frameworks. Research limitations/implications A literature review does have limitations insofar as some literature may have been missed because of different key terms. A further consideration being literature from 2019 not available at the time the review was conducted. Practical implications It represents the state of play in regard to the use of quality frameworks operating in HE and business schools. Insight is offered into how the use of continuous improvement methods can deliver quality in HE to benefit the sector, students and others. An agenda for future research is offered. Originality/value The discussion is valuable as it seeks to improve understanding of the relationships between methodologies with adopted quality frameworks in the HEI sector. A contribution is made in the use of force field analysis to represent the critical success factors and barriers of LSS in HEI.