Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1537090͔Breathers are highly localized oscillatory excitations in discrete nonlinear lattices that have been invoked as a possible way to store and transport vibrational energy in a large variety of physical and biophysical contexts. A particular scenario where the robustness and longevity of breathers has been a matter of considerable debate involves nonlinear arrays subject to thermal relaxation via the connection of surface sites to a cold environment. The important questions are these: Can breathers "created spontaneously or by design… survive for a long time in such a relaxing environment? If they can survive, can they move? We detail answers to these questions, one of which is rather unequivocal: Breathers that move do not live very long. So is another: Breathers are quite robust when they do not move. The more complicated question then deals with the conditions that allow breathers to remain stationary and undisturbed for a long time in a relaxing environment. We detail some conditions that lead to this outcome, and others that definitely do not.