LED module, arrays of LED modules, luminaires incorporating such arrays, and methods of illumination where the configuration of respective components facilitates any one or more of desired angle, location and shape of illumination provided by the LEDs. LED modules are selectively disposed on a carrier plate. Each of the LED modules includes a substantially planar LED circuit board with LED chips disposed thereon, a heat sink formed of heat transmitting material and having a mounting surface for accommodating an LED circuit board to dissipate heat from the LED chips, and a reflector with its reflective surface disposed with respect to the LED chips to direct the emitted light toward an axis of illumination extending away from and substantially perpendicular to a plane containing the planar LED circuit board. The heat sink, the LED circuit board and the reflector are arranged such that the axis of illumination is not perpendicular to a plane containing the surface illuminated by the light emitted from the LED chips.