An LED-based luminaire employs an LED module mounted to a housing. The LED module is advantageously configured to transmit heat generated by the LEDs across and/or through the module and to the housing for dispersal to the environment. LED modules can be configured with conductive or non-conductive cores, and may be configured to evacuate heat from one or both faces of the LED module. Further, multiple heat paths can be defined from components on an LED module to the housing and to the environment.