In this talk, I am going to give a brief introduction of complex Computer models, also known as simulators, that are widely used in all areas of science and technology to represent complex real-world phenomena. Simulators are often sufficiently complex that they take appreciable amounts of computer time or other resources to run. In this context, a methodology has been developed based on building a statistical representation of the simulator, known as an emulator. The principal approach to building emulators uses Gaussian processes. I am going to present a set of diagnostics to validate and assess the adequacy of a Gaussian process emulator as surrogate for the simulator. These diagnostics are based on comparisons between simulator outputs and Gaussian process emulator outputs for some test data, known as validation data, defined by a sample of simulator runs not used to build the emulator. Our diagnostics take care to account for correlation between the validation data.