This article is dedicated to the 100th anniversary of quantum mechanics, and in particular to electron spin—a phenomenon that has no counterpart in classical physics. The hypothesis of electron spin was proposed by Uhlenbeck and Goudsmit in 1925—1926 to explain numerous experimental data. Two years later, Dirac discovered the existence of electron spin when constructing the relativistic wave equation for a free particle. This came as a great surprise to Dirac, since, as he later claimed (in 1977), his goal was to obtain a relativistic wave equation for the simplest particle, which he considered to be a particle with zero spin. But it turned out that the simplest particle is one with spin 1/2.