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In solid-state physics, the phenomenon of localization is usu-ally perceived as arising from extrinsic disorder that breaks the discrete translational invariance of the perfect crystal lat-tice. Familiar examples include the localized vibrational phonon modes around impurities or defects (such as atomic vacancies or interstitial atoms) in crystals and Anderson lo-calization of electrons in disordered media.1 The usual per-ception among solid-state researchers is that, in perfect lat-tices—those free of extrinsic defects—phonons and electrons exist only in extended, plane wave states. That notion extends to any periodic structure, such as a photonic crystal or a pe-riodic array of optical waveguides. Such firmly entrenched perceptions were severely jolted in the late 1980s by the dis-covery that intrinsic localized modes2 (ILMs), also known as discrete breathers3 (DBs), are, in fact, typical excitations in perfectly periodic but strongly nonlinear systems