A systematic literature review is used to explore the relationship between complexity theory and economics. Broad search terms identify an unmanageable large number of hits. A more focused search strategy follows the PRISMA protocol and screens for Economics branded publications, and with key words for different applications of economics occurring in the abstract. This results in a distinct group of 247 publications. One hundred and twenty-two publications are excluded due to inclusion criteria or a lack of relevance. The remaining 113 are analysed for (1) use of complexity theory concepts, (2) types of methodology and methods, and (3) the applications for macro, meso, and micro issues. The publication with the greatest frequency of resulting articles is Complexity, closely followed by Ecological Economics. The highest annual citation ratio for a single article was 33.88. Complexity theory concepts included: non-linearity, system interactions, adaption, and resilience. Many developed a meso application, rather than solely focusing on macro or micro designs. Agent Based Models (ABMs) were popular, as were general systems models following the practice of the late system theorist, Donella Meadows. Applications were interdisciplinary and diverse, including world system models that linked macroeconomics to climate and sustainability, as contrast with micro and meso models trying to explain the complexity of agent-based behaviour on specific organisations or higher-level processes.