In this talk I will explain the phenomenology of the quantum phase transition in ferromagnetic metals, which commonly display a first-order transition at low temperatures, with a tricritical point and associated tricritical wings in the phase diagram, see the phase diagram of UGe2 shown below. After a general introduction to quantum phase transitions, I will show that the Third Law of Thermodynamics puts constraints on the phase diagram of such systems: The coexistence curve in zero field necessarily has an infinite slope at zero temperature, and the tricritical wings are perpendicular to the zero-temperature plane, but not to the zero-field plane. These results, which are based on the third law and basic thermodynamics only, explain existing data for many systems.