An appliance for heating and/or frothing milk, in which steam or a mixture of steam and air acting as a heat carrier is injected into the milk, with the heating unit including an inner steam channel and an outer annular channel for the milk. The outer annular channel coaxially surrounds the inner steam channel, with hot steam or a mixture of steam and air being supplied at an upstream end of the steam channel and with milk being supplied at an upstream end of the annular channel. To improve the heat output and the energy efficiency of the heating unit and to reduce the maintenance requirement, the steam channel and the annular channel are separated from one another, with their downstream ends opening out into an outlet channel for discharging the heated and/or frothed milk.