First, what follows is just what I've learned from this forum ... and because of my interpretation, may not be 1000% accurate. On the other hand, maybe this will point you in the right direction. All that follows applies to Nichia 5mm white leds. Other colors & sizes can have different specifications. The Luxeon Star also has different voltage/amperage requirements. Still, the general trends are the same.
The easiest solution is to use three NiMH or NiCd cells for 3.6 volts and wire directly to the LED with no resistor. You can also overdrive an LED with 4.5 volts from three alkaline cells and not use any resistors, but some think it's risky. LED arrays can benefit from having small dropping resistors in the circuit.
The next easiest method is to use a resistor to bring voltage in line. However, the energy blocked by a resistor is converted to heat, so it is wasted. Still, for many folks who don't want to overdrive their LED, this is the best way to deal with voltages over 3.6 volts.
From what I've been able to piece together, a DC-DC step-up converter with linear regulator is currently the most efficient solution ... hitting 85-95% efficiency. They can be a challenge to make.
There's a great deal of information available in the forums that you can find by searching. You might want to search this forum for "voltage regulators" and read the threads. There's another about voltage regulators on-going in the Batteries Included forum. The Batteries Included forum also offers information on how to determine what resistor values you should use in any application.
Hope this helps!
Mark
