Skyrmions are topological excitations that first arose in the context of particle physics. In recent years, through a series of beautiful experiments, they have become of great relevance to various condensed matter systems, particularly in magnetic materials where they may find applications in magnetic memories and spintronic devices. Momentum space skyrmions are also at the heart of the topological phases which were recently recognized with the 2016 Nobel Prize in physics. In this colloquium I will begin with a pedagogical introduction to skyrmions. I will then explain how these spin textures arise in chiral  magnets, describe their unusual properties, and conclude with some of our recent theoretical predictions [1,2,3] on how the stability of skyrmion phases can be greatly enhanced by tuning the spin-orbit coupling and magnetic anisotropy.

[1] S. Banerjee, O. Erten and M. Randeria, Nature Physics 9, 626 (2013)

[2] S. Banerjee, J. Rowland, O. Erten and M. Randeria, Phys. Rev. X 4, 031045 (2014)

[3] J. Rowland, S. Banerjee and M. Randeria, Phys. Rev. B 93, 020404(R) (2016)