GATE, the Geant4 Application for Tomographic Emission, is a simulation platform developed for PET and SPECT. It combines a powerful simulation core (the Geant4 toolkit) and a large range of developments dedicated to nuclear medicine. In particular, it models the passing of time during real acquisitions, allowing to handle dynamic systems such as decaying source distributions or moving detectors. We present several series of results that illustrate the possibilities of this new platform. The simulation of decaying sources is illustrated on a dual-isotope acquisition with multiple time-frames. Count rate curves taking into account random coincidences and dead-time are shown for a dual-crystal set-up and for a small-animal PET scanner configuration. Simulated resolution curves and reconstructed images are shown for rotating PET scanners. Lastly, we present comparisons of simulated point-spread functions and spectra with experimental results obtained from a small-animal gamma camera prototype.