High-entropy alloys (HEAs) are a relatively new class of alloys comprising multiple principal elements in high concentrations (often near-equiatomic). Some of these alloys exhibit remarkable combinations of strength, ductility, and toughness that all increase simultaneously as the temperature is reduced down to the cryogenic range. In this talk, I will review what has been learned recently about the fundamental mechanisms responsible for their mechanical properties. The focus will be on solid solution HEAs having the FCC crystal structure. High, sustained, work hardening is an important feature of all such alloys that have good strength-ductility combination. Sequential triggering of multiple deformation mechanisms, including dislocation (Taylor) hardening, twinning, and phase transformation, has been shown to postpone the onset of necking instability, thereby allowing extensive elongations before fracture and high ultimate tensile strengths. Microstructural evolution and the macroscopic flow and fracture behavior of model HEAs will be discussed and related to their governing factors such as stacking fault energy, critical stress for twinning, shear modulus, and their temperature dependences.