Magnetic skyrmions are topologically protected nano-scale spin textures. They normally exist in chiral magnets and magnetic thin films with broken inversion symmetry. The size of skyrmion ranges from 1 nm to several hundred nanometers, depending on the material parameters. The spins of skyrmion wrap around the unit sphere exactly once, thus facilitating the unit topological charge of a skyrmion. Due to their non-trivial topology, skyrmions exhibit exotic physics such as the topological Hall effect (THE) and the emergent electrodynamics. Skyrmions show particle-like dynamics and can be driven with ultra-low current density. Furthermore, they can be created, annihilated, manipulated and detected by all-electric methods, making skyrmion a promising candidate for next-generation information storage and processing technologies. On the other hand, combining skyrmions with superconductors and topological insulators may also lead to intriguing physics and applications such as the topological quantum computing. Over the past few years, the creation, annihilation and detection of skyrmion at room temperature have already been demonstrated, but the precise control of single skyrmion with size below 10 nm is still a challenge. In this paper, we first review the fundamental physics of skyrmion, from its topology to its emergent dynamics. Physical mechanisms of the Dzyaloshinskii-Moriya interaction, the emergent electrodynamics and the THE are discussed. Then the skyrmion material systems, including chiral magnets, magnetic thin films, artificial skyrmion systems, frustrated magnets, bi-skyrmion materials and antiskyrmion materials, are comprehensively summarized. The optimizations of materials and potential new skyrmion materials are also proposed for different material systems. Methods of creating, annihilating and detecting skyrmions, which also cover potential application methods other than electrical methods, are discussed from both theoretical and experimental point of view. The energy efficiencies and reliabilities of different creation and annihilation methods and the sensitivities of different detection methods are still unclear, these current bottlenecks and possible avenues towards skyrmion-based spintronics are described. Finally, we address some possible future directions of skyrmion research, such as the antiferromagnetic skyrmion and skyrmions in topological insulators, which may lead to the discovery of peculiar topological quantum physics and materials.