One-dimensional stellar evolution models have been successful at representing the structure and evolution of stars in diverse astrophysical contexts, but complications have been noted in the context of young, magnetically active stars, as well as close binary stars with significant tidal interactions. Numerous puzzles are associated with pre-main sequence and active main-sequence stars, relating to their radii, their colors, certain elemental abundances, and the coevality of young clusters, among others. A promising explanation for these puzzles is the distorting effects of magnetic activity and starspots on the structure of active stars. To assist the community in evaluating this hypothesis, we present the Stellar Parameters Of Tracks with Starspots (SPOTS) models, a grid of solar-metallicity stellar evolutionary tracks and isochrones which include a treatment of the structural effects of starspots. The models range from 0.1-1.3M and from spot-less to a surface covering fraction of 85%, and are evolved from the pre-main sequence to the red giant branch (or 15 Gyr). We also produce two-temperature synthetic colors for our models using empirically-calibrated color tables. We describe the physical ingredients included in the SPOTS models and compare their predictions to other modern evolution codes. Finally, we apply these models to several open questions in the field of active stars, including the radii of young eclipsing binaries, the color scale of pre-main sequence stars, and the existence of sub-subgiants, demonstrating that our models can explain many peculiar features of active stars.