Skyrmions are topological solitons that were first discussed in quantum field theory in the 1960’s. In recent years, through a series of beautiful experimental developments, they have become of great relevance to various condensed matter systems, particularly in the form of topological spin textures in magnetic materials.
I will begin with a pedagogical introduction to skyrmions and explain how these spin textures arise in magnets with broken inversion symmetry. I will then describe their unusual properties and potential for applications. I will 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.
 S. Banerjee, O. Erten and M. Randeria, Nature Physics 9, 626 (2013)
 S. Banerjee, J. Rowland, O. Erten and M. Randeria, Phys. Rev. X 4, 031045 (2014)
 J. Rowland, S. Banerjee and M. Randeria, Phys. Rev. B 93, 020404(R) (2016)