  Kitaev's honeycomb-lattice compass model describes a spin liquid with
emergent fractionalized excitations. Here we study the physics of isolated
magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this
Kondo-type problem in terms of a many-state quantum impurity coupled to a
multichannel bath of Majorana fermions and present the numerically exact
solution using Wilson's numerical renormalization group technique. Quantum
phase transitions occur as a function of Kondo coupling and locally applied
field. At zero field, the impurity moment is partially screened only when it
binds an emergent gauge flux, and otherwise becomes free at low temperatures.
We show how Majorana degrees of freedom determine the fixed-point properties,
make contact with Kondo screening in pseudogap Fermi systems, and discuss
effects away from the dilute limit.
