We study the production of direct photons in e+e- annihilation e+e- → γ + hadrons, where the high-energy photon is emitted at a large angle to a hadron jet or is a fragment of the jet itself. We give the angle and energy dependence of the cross section for photons radiated from the final-state quarks, the initial-state leptons, and also the interference term. Large angle radiation by the quarks is only mildly affected by QCD corrections to the parton model. For photons radiated within or near a jet axis, however, the gluon radiative corrections can be large. We study the phenomenological implications of these corrections at present and future energies. Direct photon production affords a unique view into the short- and long-distance processes of jet formation. It can help clarify the space-time transition between perturbative and non-perturbative processes in jet development.