Rules
There are several rules that deal with fluorescence. The Kasha�Vavilov rule dictates that the quantum yield of luminescence is independent of the wavelength of exciting radiation. This is not always true and is violated severely in many simple molecules. A somewhat more reliable statement, although still with exceptions, would be that the fluorescence spectrum shows very little dependence on the wavelength of exciting radiation.
The Jablonski diagram describes most of the relaxation mechanisms for excited state molecules.