Deep penetration welding and cutting of metals can be carried out at high speed with relatively low laser power. The efficient coupling of the laser radiation to the metal is due to the formation of a "keyhole." Over the years, an attempt has been made to transfer the results on metals to plastics. It will be shown here that keyhole welding of plastics is limited to the very restricted set of plastics that have a boiling point. Volume heating, a mechanism that is not applicable to metals, is restricted to plastics with a good transparency for the incident radiation and with a high optical quality. Finally, surface heating is shown to be the most common mechanism for heating plastics.