Oka theory is about the validity of the h-principle in complex analysis and geometry. In this expository lecture, I will trace its main developments, from the classical results of Kiyoshi Oka (1939) and Hans Grauert (1958), through the seminal work of Mikhail Gromov (1989), to the introduction of Oka manifolds (2009) and the present state of knowledge. The lecture does not assume any prior exposure to this theory.
