  Localized phenomena abound in nature and throughout the physical sciences.
Some universal mechanisms for localization have been characterized, such as in
the snaking bifurcations of localized steady states in pattern-forming partial
differential equations. While much of this understanding has been targeted at
steady states, recent studies have noted complex dynamical localization
phenomena in systems of coupled oscillators. These localized states can come in
the form of symmetry-breaking chimera patterns that exhibit a coexistence of
coherence and incoherence in symmetric networks of coupled oscillators and gap
solitons emerging in the band gap of parametrically driven networks of
oscillators. Here, we report detailed numerical continuations of localized
time-periodic states in systems of coupled oscillators, while also documenting
the numerous bifurcations they give way to. We find novel routes to
localization involving bifurcations of heteroclinic cycles in networks of Janus
oscillators and strange bifurcation diagrams resembling chaotic tangles in a
parametrically driven array of coupled pendula. We highlight the important role
of discrete symmetries and the symmetric branch points that emerge in symmetric
models.
