  Point-like motile topological defects control the universal dynamics of
diverse two-dimensional active nematics ranging from shaken granular rods to
cellular monolayers. A comparable understanding in higher dimensions has yet to
emerge. We report the creation of three-dimensional active nematics by
dispersing extensile microtubule bundles in a passive colloidal liquid crystal.
Light-sheet microscopy reveals the millimeter-scale structure of active
nematics with a single bundle resolution and the temporal evolution of the
associated nematic director field. The dominant excitations of
three-dimensional active nematics are extended charge-neutral disclination
loops that undergo complex dynamics and recombination events. These studies
introduce a new class of non-equilibrium systems whose turbulent-like dynamics
arises from the interplay between internally generated active stresses, the
chaotic flows and the topological structure of the constituent defects.
