Do we live in a quantum universe? Or a classical relativistic universe? Or a universe that is somehow a hybrid of the two? The papers collected in Quantum Heresies argue that it is quantum all the way down, and probably all the way up, too. Peacock criticizes the orthodox view that quantum mechanics and relativity stand in a relation of 'peaceful coexistence', and argues that new concepts of simultaneity are needed in order to think about time and causation in the radically nonlocal world that quantum mechanics reveals. Papers in collaboration with John Woods and Brian Hepburn explore the logic of quantum mechanics and the dynamics of entangled states, and an Envoi points to the work still to be done.