Approximate Bayesian Computation (ABC) arose in response to the difficulty of simulating observations from posterior distributions determined by intractable likelihoods. The method exploits the fact that while likelihoods may be impossible to compute in complex probability models, it is often easy to simulate observations from them. ABC in its simplest form proceeds as follows: (i) simulate a parameter from the prior; (ii) simulate observations from the model with this parameter; (iii) accept the parameter if the simulated observations are close enough to the observed data. The magic, and the source of potential disasters, is in step (iii). This talk will outline what we know (and don't!) about ABC and illustrate the methods with applications to the fossil record and stem cell biology.