CNC Laser cutters are almost magical. They use a tightly focused beam of light to cut through a wide range of materials, leaving a kerf (the area cut away by the laser) of just a few thousandths of a inch. The main limitation of a laser cutter is the depth that it can cut. The depth of the cut is directly related to the power of the laser beam (expressed in watts, just like a light bulb). Unfortunately, the price of the laser unit goes up exponentially as the wattage increases.
For a practical machine, that will cut through 1/8 inch thick wood, plastics, etc., you'll need a laser in the 35 to 50 watt range. These type lasers will cost around $5,000. The mechanism that drives a laser cutter can be very much like a CNC router, and it is actually possible to have interchangeable "heads" to switch from routing to laser cutting.
Keep in mind though, that just like a CNC plasma cutter, a laser cutter can only do two dimensional cutting.... cutting parts from thin sheet stock. The reality is that unless you plan to do production work, you can get almost the same results with a CNC router, using very small diameter router bits. A .030 inch diameter router bit will cut an almost square corner, with a very small kerf. This is easily usable for cutting model airplane parts from balsa wood or thin plywood, etc.