In accordance with the present invention, methods and apparatus to control the combustion of a burner are presented which overcome many of the problems of the prior art. One aspect of the invention comprises a burner control apparatus including a device for viewing light emitted by a flame from a burner, a device for optically transporting the viewed light into an optical processor, an optical processor for processing the optical spectrum into electrical signals, a signal processing for processing the electrical signals obtained from the optical spectrum, and a control device which accepts the electrical signals and produces an output acceptable to one or more oxidant or fuel flow control devices. The control device, which may be referred to as a "burner computer," functions to control the oxidant flow and/or the fuel flow to the burner. In a particularly preferred apparatus embodiment of the invention, a burner and the burner control apparatus are integrated into a single unit, which may be referred to as a "smart" burner.