High-entropy alloys (HEAs) are a class of new metallic materials that have revolutionized alloy design over the past ten years. Unlike conventional alloys with one and rarely two base elements, HEAs contain multiple principal elements (at least four principal elements) with equal or nearly equal atomic concertation to promote the formation of simple solid solution phases. Due to the presence of multiple principal elements, multiple deformation mechanisms (including dislocation activities, deformation twinning, and phase transformation) activate during deformation of HEAS. Therefore, HEAs usually exhibited many excellent mechanical properties, such as ultrahigh hardness, high tensile strength, good ductility, high thermal softening resistance, remarkable irradiation resistance, and good wear resistance. HEAs are thought to be the most promising structure materials and have attracted tremendous attention over worldwide in the fields of solid mechanics and material sciences. In this review paper, we first briefly introduce the unique and complicated microstructural features of HEAs, i.e. HEAs have both chemically short-range orderings and severe lattice distortion. Then, we review the recent experimental studies on mechanical properties, behaviors and deformation mechanisms of HEAs with face-centered cubic, body-centered cubic, hexagonal close-packed, dual or meta-stable phases. We also mainly emphasize some effective strengthening and toughening strategies, including solid solution, grain refinement, second phase or precipitation. We further summarize some advanced atomistic simulations/modelling on microstructures, mechanical properties and deformation of various HEAs. Finally, we address a list of open problems and challenges for the future studies about design, fabrication and mechanics of HEAs, and provide some important mechanistic insights into design and fabrication of HEAs with excellent mechanical properties and performances.