Three different types of optical phenomena have been observed at high altitude above thunderstorms: an enhanced airglow (''elves'') at roughly ~90 km; a reddish glow (''sprites'') from 50 to 90 km; and an upward moving, bluish emission (''jets'') below 40 km. A likely explanation for some or all of these phenomena is gas breakdown caused by the electromagnetic fields of lightning discharges. This paper examines the connection between these fields and breakdown at high altitude, using both analytic models and numerical simulations. Included in the calculations are the radiation fields from the lightning return stroke and the quasi-static fields from the continuing current. The different nature of the two fields is shown to produce two distinct types of breakdown, with characteristics similar to those of elves and sprites. Also mentioned is a third breakdown mechanism which may account for blue jets.