I will explain what I call the `Koszul mirror principle', which roughly says that perturbations of the differential on a Koszul algebra (over some Koszul operad) correspond to deformations of the algebraic structure on the Koszul dual algebra, in a way which preserves the Koszul duality relation. This leads to the notion of `minimal Koszul models' for algebras over the given operad, generalizing minimal free models. Applications include calculation of L-infinity algebra structures on rational homotopy groups of spaces that admit tractable Koszul models and construction of small A-infinity algebra models for Hochshild cochains of dg-algebras.