This review gives an overview of the quantum phase transition (QPT) problem in metallic ferromagnets, discussing both experimental and theoretical aspects. These QPTs can be classified with respect to the presence and strength of quenched disorder: Clean systems generically show a discontinuous, or first-order, QPT from the ferromagnetic state to a paramagnetic one as a function of some control parameter, as predicted by theory. Disordered systems are much more complicated, depending on the disorder strength and the distance from the QPT. In many disordered materials the QPT is continuous, or second order, and Griffiths-phase effects coexist with QPT singularities near the transition. In other systems the transition from the ferromagnetic state at low temperatures is to a different type of long-range order, such as an antiferromagnetic or a spin-density-wave state. In still other materials a transition to a state with glass-like spin dynamics is suspected. The review provides a comprehensive discussion of the current understanding of these various transitions, and of the relation between experimental and theoretical developments.