Testing the limits of quantum mechanics: motivation, state of play, prospects

I present the motivation for experiments which attempt to generate, and verify the existence of, quantum superpositions of two or more states which are by some reasonable criterion `macroscopically' distinct, and show that various a priori objections to this programme made in the literature are flawed. I review the extent to which such experiments currently exist in the areas of free-space molecular diffraction, magnetic biomolecules, quantum optics and Josephson devices, and sketch possible future lines of development of the programme.