Strong lensing at the galaxy scale is useful for numerous applications in Astrophysics and Cosmology. Some of the principal applications are studying the mass structure, formation, and evolution of elliptical galaxies, constraining the stellar initial mass function, and measuring cosmological parameters. Since the first discovery of a galaxy-scale strong lens in the eighties, this field has come a long way regarding data quality and techniques to model the data. In this review article, we describe the most common methodologies to model lensing observables of galaxy-scale strong lenses, especially the imaging data, as it is the most available and informative source of lensing observables. We review the main results from the literature in astrophysical and cosmological applications of galaxy-scale strong lenses. We also discuss the current limitations of the data and methodologies and provide a future outlook of the expected development and improvements in both aspects in the near future.