The phenomenon of power law decays in molecular beams is reviewed. The transition from a canonical to a microcanonical description of the decay is analyzed, and the appearance of the power law decay derived. Deviations from a power law often contain information on parallel competing processes. This is illustrated with examples where thermal radiation or dark unimolecular channels are the competing processes. Also corrections to the power law due to finite heat capacities and from nonideal energy distributions are derived. Finally, the consequences for the interpretation of action spectroscopy data are reviewed. © 2020 The Authors. Mass Spectrometry Reviews published by John Wiley & Sons Ltd. Mass Spec Rev