BACKGROUND: Glucagon-like peptide 1 (GLP-1) is a hormone that promotes insulin secretion, delays gastric emptying, and inhibits glucagon secretion. The GLP-1 receptor agonists have been developed as adjunctive therapies for type 2 diabetes to improve glucose control. Recently, there has been an interest in introducing GLP-1 receptor agonists as adjunctive therapies in type 1 diabetes alongside automatic insulin delivery systems. The preclinical validation of these systems often relies on mathematical simulators that replicate the glucose dynamics of a person with diabetes. This review aims to explore mathematical models available in the literature to describe GLP-1 effects to be used in a type 1 diabetes simulator. METHODS: Three databases were examined in the search for GLP-1 mathematical models. More than 1500 works were found after searching for specific keywords that were narrowed down to 39 works for full-text assessment. RESULTS: A total of 23 works were selected describing GLP-1 pharmacokinetics and pharmacodynamics. However, none of the found models was designed for type 1 diabetes. An analysis is included of the available models' features that could be translated into a GLP-1 receptor agonist model for type 1 diabetes. CONCLUSION: There is a gap in research in GLP-1 receptor agonists mathematical models for type 1 diabetes, which could be incorporated into type 1 diabetes simulators, providing a safe and inexpensive tool to carry out preclinical validations using these therapies.