High-entropy alloys (HEAs), also known as multi-principal element alloys or multi-component alloys, have been the subject of numerous investigations since they were first described in 2004. The earliest HEA was the equiatomic CrMnFeCoNi "Cantor" alloy, but HEM now encompass a broad class of metallic and ceramic systems. The concept of utilizing the high entropy of mixing to develop stable multi-element alloys may not be scientifically correct but has produced extraordinary mechanical properties in specific HEAs, mainly CrCoNi-based alloys, associated with their continuous work-hardening rate that is sustained to large plastic strains (similar to 0.5) and at low temperatures. This, in combination with the high frictional forces on dislocations and a propensity for twinning, leads to outstandingly high fracture toughness values (exceeding 200 MPa.m(1/2)) and resistance to shear-band formation under dynamic loading. The critical shear strain for the onset of adiabatic shear band formation is similar to 7 for the Cantor alloy, much higher than that for conventional alloys, suggesting superior ballistic properties. The slower diffusion rates resulting from the multi-element environment contribute to the excellent intermediate temperature performance. We review the principal mechanical properties of these alloys with emphasis on the face-centered cubic systems, such as the CrCoNi-based alloys. Their favorable mechanical properties and ease of processing by conventional means suggest extensive utilization in many future structural applications.