Abstract: Quantization was invented (under the name “Umdeutung”) by Heisenberg in 1925. Operator algebras were introduced by von Neumann in the 1930s, partly inspired by quantum theory. However, the precies connection between these topics was only unearthed by Rieffel and others in the 1990s, involving deformation theory as well as Lie groupoids. This picture is now complete. The talk should be accessible to everyone who knows what a Hilbert space is.