This book has been about quantum mechanical models compatible with the Galilean Principle of Relativity (though we usually worked in a fixed inertial frame), and we know that this must be replaced by Einstein’s Special Theory of Relativity if we want results accurate to better than v∕c where v is the speed of the fastest particle participating in the process under study. c is of course the speed of light, c = 3 × 108 m/s. In this short chapter, we want to indicate the remarkable complications that result from insisting that quantum mechanics (QM) be invariant under Lorentz transformations.