One of the major goals of palaeontology is the reconstruction of life on earth at specific times in the past. The major pieces of evidence that we can use to help with this process are the bodies and traces of the animals and plants that are preserved as fossils within the rocks from the various geological epochs. However whilst this tells us about the shapes of past organisms we need to use other approaches to more completely understand what these organisms were like. Synthetic palaeontology attempts to rebuild fossils as living creatures, most commonly as in silico simulations at either the organismal or population level, and can be used to directly test hypotheses about extinct animals. Examples include discovering at what point in human evolution our ancestors started to walk in a fully upright fashion, and deciding whether or not the largest of the predatory dinosaurs, Tyrannosaurus rex, was a pursuit hunter. Multi-physics, multi-objective simulation approaches allow evidence from a range of sources to be brought together and provide concrete predictions that can often be ground-truthed using comparative work on modern animals. Ultimately we will be able to model whole ecosystems and this will maximise the predictive power of the available evidence and help answer some of the major questions that we have about the evolutionary narrative of life on earth.