Skyrmions are topological solitons that first arose in high-energy physics. In recent years, through a series of beautiful experimental developments, they have become of great relevance to various condensed matter systems, particularly chiral magnetic materials. In this colloquium, I will begin with a pedagogical introduction to skyrmions and explain how these topological spin textures arise in magnets with spin-orbit coupling and broken inversion symmetry. I will describe the unusual properties of skyrmions and their potential for applications. I will then turn to our recent theoretical results on how skyrmion can be stabilized by tuning material parameters and geometry, and conclude with an overview of the experimental activity on skyrmions at Ohio State.