Glucagon-like peptide-1 (GLP-1) receptor agonists are a new class of antihyperglycemic drugs that enhance appropriate pancreatic β-cell secretion, pancreatic α-cell (glucagon) suppression, decrease liver glucose production, increase satiety through their action on the central nervous system, slow gastric emptying time, and increase insulin action on peripheral tissue. They are effective in the management of type 2 diabetes mellitus and have a favorable effect on weight loss. Their cardiovascular and renal safety has been extensively investigated and confirmed in many clinical trials. Recently, evidence has shown that in addition to the existing approaches for the treatment of obesity, semaglutide in higher doses promotes weight loss and can be used as a drug to treat obesity. However, some T2DM and obese patients do not achieve a desired therapeutic effect of GLP-1 receptor agonists. This could be due to the multifactorial etiologies of T2DM and obesity, but genetic variability in the GLP-1 receptor or signaling pathways also needs to be considered in non-responders to GLP-1 receptor agonists. This review focuses on the pharmacological, clinical, and genetic factors that may influence the response to GLP-1 receptor agonists in the treatment of type 2 diabetes mellitus and obesity.