Stress urinary incontinence (SUI) is a common and burdensome condition. Because of the large knowledge gap around the molecular processes involved in its pathophysiology, the aim of this review was to provide a systematic overview of genetic variants, gene and protein expression changes related to SUI in human and animal studies. On 5 January 2021, a systematic search was performed in Pubmed, Embase, Web of Science, and the Cochrane library. The screening process and quality assessment were performed in duplicate, using predefined inclusion criteria and different quality assessment tools for human and animal studies respectively. The extracted data were grouped in themes per outcome measure, according to their functions in cellular processes, and synthesized in a narrative review. Finally, 107 studies were included, of which 35 used animal models (rats and mice). Resulting from the most examined processes, the evidence suggests that SUI is associated with altered extracellular matrix metabolism, estrogen receptors, oxidative stress, apoptosis, inflammation, neurodegenerative processes, and muscle cell differentiation and contractility. Due to heterogeneity in the studies (e.g., in examined tissues), the precise contribution of the associated genes and proteins in relation to SUI pathophysiology remained unclear. Future research should focus on possible contributors to these alterations.