A system may have lights. The lights may emit visible and infrared light. Infrared light may be used to illuminate objects that are monitored using infrared image sensors or other infrared sensors. Visible light may be used to illuminate objects that are viewed by users and which may be monitored using sensors. The lights may be adjustable. An adjustable light may have a light source that contains an infrared light-emitting device such as an infrared light-emitting diode and a visible light-emitting device such as a visible light-emitting diode. A reflector may reflect light from the light source towards a lens. An adjustable light-blocking device may be located between the reflector and the lens. The light-blocking device may allow infrared light to pass unimpeded while adjusting visible light passing to the lens.