Symmetry breaking together with strong spin-orbit interaction give rise to many exciting phenomena within condensed matter physics. A recent example is the existence of chiral spin textures, which are observed in magnetic systems lacking inversion symmetry. These chiral spin textures, including domain walls and magnetic skyrmions, are both fundamentally interesting and technologically promising. For example, they can be driven very efficiently by electrical currents, and exhibit many new physical properties determined by their real-space topological characteristics. Depending on the details of the competing interactions, these spin textures exist in different parameter spaces. However, the governing mechanism underlying their physical behaviors remain essentially the same. In this review article, the fundamental topological physics underlying these chiral spin textures, the key factors for materials optimization, and current developments and future challenges will be discussed. In the end, a few promising directions that will advance the development of skyrmion based spintronics will be highlighted.

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