  Gamma-ray bursts (GRBs) have been an enigma since their discovery forty years
ago. However, considerable progress unraveling their mysteries has been made in
recent years. Developments in observations, theory, and instrumentation have
prepared the way so that the next decade can be the one in which we finally
answer the question, "What are gamma-ray bursts?" This question encompasses not
only what the progenitors are that produce the GRBs, but also how the enormous
luminosity of the GRBs, concentrated in gamma rays, is achieved. Observations
across the electromagnetic spectrum, from both the ground and space, will be
required to fully tackle this important question. This white paper, mostly
distilled from a recent study commissioned by the Division of Astrophysics of
the American Physical Society, focuses on what very high energy (~100 GeV and
above) gamma-ray observations can contribute. Very high energy gamma rays probe
the most extreme high energy particle populations in the burst environment,
testing models of lepton and proton acceleration in GRBs and constraining the
bulk Lorentz factor and opacity of the outflow. Sensitivity improvements of
more than an order of magnitude in the very high energy gamma-ray band can be
achieved early in the next decade, in order to contribute to this science.
