In 1985 the Nobel Prize in physics was awarded to Klaus von Klitzing for the discovery of the integer quantum Hall effect. This did not mark the end but rather the beginning of a new chapter in solid state physics since quantum Hall physics had more surprises in store. The fractional quantum Hall effect was discovered by Robert B. Laughlin, Horst L. Störmer, and Daniel C. Tsui in the 1980s, who were awarded the Nobel Prize in physics for the discovery of this hallmark of many-body physics in 1998. The lecture draws a line from the classical Hall effect to the integer and the fractional quantum Hall effect. The basic concepts of the underlying physics are highlighted and the tremendous impact of quantum Hall physics on electrical metrology is addressed. Nowadays, the quantum Hall effect provides highly precise and universal quantum standards of electrical resistance based on the elementary charge and Planck´s constant.