The study of dinosaurs has been through a revolution in recent decades. The story began half a century ago, when Robert McNeill Alexander, a professor of zoology at the University of Leeds, showed how the speed of an animal could be calculated from the spacing of its footprints and its body size.This formula worked both for modern and extinct animals and so, for the first time, the speed of a dinosaur could be estimated from a fossilised trackway. Alexander calculated speeds for different dinosaurs of between 1.0 and 3.6 metres per second (up to 13kmh) – rather slower than others had guessed.In the 1970s, dinosaurs were becoming exciting again after years of being treated as lumbering failures. Termed the “dinosaur renaissance”, American paleontologists Robert Bakker and John Ostrom were among those transforming understanding by arguing that dinosaurs were active, possibly warm-blooded, and that they included the ancestors of birds. Remarkable fossils of feathered dinosaurs from China, found from 1996 onwards, cemented this idea.Before Alexander’s groundbreaking study in 1976, palaeontologists had made “reasonable guesses” about the function of dinosaurs – persuasive arguments but often untestable. Alexander began a movement to apply scientific methods to investigating dinosaur function and behaviour.His research heralded the start of a revolution in palaeobiological methods, using modern scientific methods to bring dinosaurs to life in a testable way.Modern techniques applied to the deep pastThere are many questions about dinosaurian palaeobiology: what colours were they, how fast did they run, how did their jaws operate, how long did they take to grow to adult size?Modern palaeobiologists conduct a three-step process to answer such questions. First, observe the fossil, then apply what we call the neontological toolkit – sets of observations and rules from the modern world that can be applied to ancient situations – and finally, make an inference about the dinosaur’s behaviour.To establish the running speed of dinosaurs from fossilised dinosaur tracks, Alexander measured the tracks, applied the formula derived from modern animals, and presented the speed calculation. He showed definitively that large dinosaurs could not gallop at the speed of a racehorse, as some had suggested.A more recent example by one of us (Emily) is the use of engineering methods to establish dinosaurs’ jaw movements. The computational methods are identical to those used to design aircraft, buildings and medical limb replacement devices, and so they are all stress-tested and they work. By making a 3D model of a skull or skeleton, the dinosaur’s jaw movements and forces, as well as leg movements, could be calculated.Feeding calculations show that some flesh-eating dinosaurs punctured bone, while others pulled at their dead prey to yank off chunks of flesh. The most famous dinosaurian flesh eater, Tyrannosaurus rex, bit with a force of 50,000 newtons – enough to have bitten a car in half. Video: CBBC. Scanning can reveal embryonic dinosaurs inside their eggs, and sections through their bones show growth rings that tell us their age at death. This means palaeontologists can calculate the rate of growth of dinosaurs and indeed some of them, during growth spurts, were putting on as much as 1-2 tonnes a year.Earlier calculations suggested T. rex reached adult size of 6-8 tonnes at 20 years, but re-examination by Holly Woodward and colleagues suggests more like 30 years. This revision is not based on guesswork, but on counting bone rings and estimating body masses from a larger sample of specimens than first used.But what about their colours? Even here, the new wave of investigative palaeontology has revealed the answer. In 2010, in work done between Bristol, Beijing and Yale University, the colours and colour patterns of two small theropod dinosaurs, Sinosauropteryx and Anchiornis, were published.The neontological toolkit here was from modern birds, whose melanosomes (tiny capsules inside their feathers) contain variants of the pigment melanin. Two types of melanin give either black, brown and grey colours or ginger colours, and each type is contained in a differently shaped capsule.These shapes were preserved in the dinosaurs’ fossil feathers. Details of their coloured crests and wing and tail feather stripes show that small dinosaurs at least used these colours in competitive displays, just like some modern birds.We don’t need a time machineAll these studies are scientific hypotheses that can be disproved by contrary evidence. We don’t need a time machine to determine, say, that the small Chinese dinosaur Sinosauropteryx had a ginger-and-white striped tail, or that T. rex could run at a range of speeds from 16 to 40 kilometres per hour.Anyone who disagrees with these findings simply has to provide a critique of the chain of evidence to identify where an error has been made. But this scientific revolution in dinosaur studies does not mean every question about them has been answered.For example, we don’t yet know the sounds dinosaurs made, nor exactly how they communicated with each other. In some cases, researchers have reconstructed the nasal passages and discovered what toots and honks some dinosaurs made – but we cannot be sure these are realistic.What are the limits of our knowledge about dinosaurs? It would be wise to be cautious in our predictions. After all, it was once widely claimed we would never know their true colours. A new generation of smart investigators may soon identify new toolkits that solve many more questions about these extraordinary creatures.Emily Rayfield receives funding from UK research councils NERC and BBSRC. Michael J. Benton does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.