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Purpose: The purpose of this paper is twofold: (1) to map and analyze existing complexity typologies and (2) to develop a framework for characterizing complexity-based approaches. Design/methodology/approach: This study was conducted in three stages: (1) initial identification of typologies related to complexity following a structured procedure based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol; (2) backward and forward review to identify additional relevant typologies and (3) content analysis of the selected typologies, categorization and framework development. Findings: Based on 17 selected typologies, a comprehensive overview of complexity studies is provided. Each typology is described considering key concepts, contributions and convergences and differences between them. The epistemological, theoretical and methodological diversity of complexity studies was explored, allowing the identification of the main schools of thought and authors. A framework for characterizing complexity-based approaches was proposed including the following perspectives: ontology of complexity, epistemology of complexity, purpose and object of interest, methodology and methods and theoretical pillars. Originality/value: This study examines the main typologies of complexity from an integrated and multidisciplinary perspective and, based on that, proposes a novel framework to understanding and characterizing complexity-based approaches. [ABSTRACT FROM AUTHOR]