We introduce the notion of a differential torsor, as a generalization of (the spectrum of) a Picard-Vessiot ring. This facilitates the use of methods of algebraic geometry in differential Galois theory. In particular, we obtain patching results for differential torsors that can be used to construct PV extensions with desired properties. As an application to function fields over the complex numbers, we obtain solutions to all complex differential embedding problems. This is joint work with Annette Bachmayr, Julia Hartmann, and Michael Wibmer.