GNSS ambiguity resolution is the process of resolving the unknown cycle ambiguities of the double-differenced carrier phase data as integers. It is the key to fast and high precision relative GNSS positioning. Ambiguity resolution applies to a great variety of GNSS models currently in use. They may range from single-baseline models used for kinematic positioning to multi-baseline models used as a tool for studying geodynamic phenomena. Depending on the application at hand, each of these models may differ in the way the reference systems and orbits are treated, or in the way the receiver and propagation delays are modelled. Despite the differences in application of the various GNSS models, their ambiguity resolution problems are intrinsically the same. In this talk we will try to sketch a theoretical framework for GPS ambiguity resolution, present some results and discuss some open problems.