Terrestrial gamma-ray flashes (TGFs) are brief flashes of gamma-rays originating in the Earth's atmosphere and observed by satellites. First observed in 1994 by the Burst And Transient Source Experiment on board the Compton Gamma-Ray Observatory, TGFs consist of one or more ˜1 ms pulses of gamma-rays with a total fluence of ˜1/cm2, typically observed when the satellite is near active thunderstorms. TGFs have subsequently been observed by other satellites to have a very hard spectrum (harder than dN/d E ∝ 1/ E ) that extends from below 25 keV to above 20 MeV. When good lightning data exists, TGFs are closely associated with measurable lightning discharge. Such discharges are typically observed to occur within 300 km of the sub-satellite point and within several milliseconds of the TGF observation. The production of these intense energetic bursts of photons is the puzzle addressed herein. The presence of high-energy photons implies a source of bremsstrahlung, while bremsstrahlung implies a source of energetic electrons. As TGFs are associated with lightning, fields produced by lightning are naturally suggested to accelerate these electrons. Initial ideas about TGF production involved electric fields high above thunderstorms as suggested by upper atmospheric lightning research and the extreme energies required for lower-altitude sources. These fields, produced either quasi-statically by charges in the cloud and ionosphere or dynamically by radiation from lightning strokes, can indeed drive TGF production, but the requirements on the source lightning are too extreme and therefore not common enough to account for all existing observations. In this work, studies of satellite data, the physics of energetic electron and photon production, and consideration of lightning physics motivate a new mechanism for TGF production by lightning current pulses. This mechanism is then developed and used to make testable predictions. TGF data from satellite observations are compared to the results of Monte Carlo simulations of the physics of energetic photon production and propagation in air. These comparisons are used to constrain the TGF source altitude, energy, and directional distribution, and indicate a broadly-beamed low-altitude source inconsistent with production far above thunderstorms as previously suggested. The details of energetic electron production by electric fields in air are then examined. In particular, the source of initial high-energy electrons that are accelerated and undergo avalanche multiplication to produce bremsstrahlung is studied and the properties of these initial seed particles as produced by cosmic rays are determined. The number of seed particles available indicates either extremely large amplification of the number of seed particles or an alternate source of seeds. The low-altitude photon source and alternate source of seed particles required by these studies suggest a production mechanism closely-associated with lightning. A survey of lightning physics in the context of TGF emission indicates that current pulses along lightning channels may trigger TGF production by both producing strong electric fields and a large population of candidate seed electrons. The constraints on lightning physics, thunderstorm physics, and TGF physics all allow production by this mechanism. A computational model of this mechanism is then presented on the basis of a method of moments simulation of charge and current on a lightning channel. Calculation of the nearby electric fields then drives Monte Carlo simulations of energetic electron dynamics which determine the properties of the resulting bremsstrahlung. The results of this model compare quite well with satellite observations of TGFs subject to requirements on the ambient electric field and the current pulse magnitude and duration. The model makes quantitative predictions about the TGF source altitude, directional distribution, and lightning association that are in overall agreement with existing TGF observations and may be tested in more detail in future experiments.