An LED light bulb has a light emitting bulb part 22 which comprises a central core 24 running from the top towards the bottom and which provides an open passageway at least at the top. The LEDs are mounted in thermal contact around the central core 24. This design provides an air flow to promote cooling of the LEDs. This in turn enables a reduced size and cost of the heat sink, or avoids the need for a heat sink altogether.