A magnetic skyrmion is a local whirl of the spin configuration in a magnetic material. As shown in FIG. 1, the spins inside a skyrmion rotate progressively with a fixed chirality from the up direction at one edge to the down direction at the centre, and then to the up direction again at the other edge. There are two typical types of magnetic skyrmions: Néel-type (FIG. 1a) and Bloch-type skyrmions (FIG. 1b), which correspond to different symmetries of the interaction between spins (this can be due to the underlying crystal lattice or to the presence of an interface, for instance), resulting in different directions of the rotation. In most systems, the spin configuration of skyrmions is determined by chiral interactions of the Dzyaloshinskii-Moriya type 1,2. Even though other types of localized whirling magnetic textures, such as magnetic bubbles, can be stabilized without Dzyaloshinskii-Moriya interactions (DMIs)-for example, they can be stabilized solely by dipolar interactions-a crucial difference is that they do not have the defined chirality that is the basis of most properties of skyrmions 3-5. Skyrmions can, indeed, be defined by the topological number S (or skyrmion number), which is a measure of the winding of the normalized local magnetization, m. In the two-dimensional limit, the topological number is: S = 1 4π ∫m·(∂ x m × ∂ y m)dxdy = ±1 (1) The normalized magnetization can be mapped on a unit sphere and, in the case of skyrmions, it covers the entirety of the sphere (4π) and is thus quantized. This non-trivial topology governs some of the most important properties of skyrmions 6. In particular, it gives rise to a topological protection of the spin configuration, as this cannot be twisted continuously to result in a magnetic configuration with different S (for example, a uniformly magnetized one); a topological barrier stabilizes the skyrmion 7. Finally, a crucial property of magnetic skyrmions is their solitonic nature: their finite extension allows them to move or interact as particles and to be excited at specific dynamical modes. Hence, the dynamics of these objects can be harnessed in devices, as will be discussed in more detail later. Magnetic skyrmions were initially identified in single crystals of magnetic compounds with a non-centrosym-metric lattice 8,9 and explained by the existence of DMIs induced by spin-orbit coupling in the absence of inversion symmetry in the crystal lattice. Skyrmions were then observed in ultrathin magnetic films epitaxially grown on heavy metals, which are subject to large DMIs induced by the breaking of inversion symmetry at the interface and to the strong spin-orbit coupling of the neighbouring heavy metal. The first investigated systems in this class were Fe monolayers and PdFe bilayers on Ir(111); the DMI can be large at the Fe/Ir(111) interface 10. Skyrmions in these systems are extremely small, extending over only a few lattice parameters (FIG. 1c). However, the stabilization of the skyrmion lattice phase necessitates large magnetic fields (of the order of 1 T) Abstract | Magnetic skyrmions are small swirling topological defects in the magnetization texture. Their stabilization and dynamics depend strongly on their topological properties. In most cases, they are induced by chiral interactions between atomic spins in non-centrosymmetric magnetic compounds or in thin films with broken inversion symmetry. Skyrmions can be extremely small, with diameters in the nanometre range, and behave as particles that can be moved, created and annihilated, which makes them suitable for 'abacus'-type applications in information storage and logic technologies. Until recently, skyrmions had been observed only at low temperature and, in most cases, under large applied magnetic fields. An intense research effort has led to the identification of thin-film and multilayer structures in which skyrmions are now stable at room temperature and can be manipulated by electrical currents. The development of skyrmion-based topological spintronics holds promise for applications in the mid-term furure, even though many challenges, such as the achievement of writing, processing and reading functionalities at room temperature and in all-electrical manipulation schemes, still lie ahead. REVIEWS NATURE REVIEWS | MATERIALS VOLUME 2 | ARTICLE NUMBER 17031 | 1 © 2 0 1 7 M a c m i l l a n P u b l i s h e r s L i m i t e d , p a r t o f S p r i n g e r N a t u r e. A l l r i g h t s r e s e r v e d .