  This paper presents the results of a search for generic short-duration
gravitational-wave transients in data from the third observing run of Advanced
LIGO and Advanced Virgo. Transients with durations of milliseconds to a few
seconds in the 24--4096 Hz frequency band are targeted by the search, with no
assumptions made regarding the incoming signal direction, polarization or
morphology. Gravitational waves from compact binary coalescences that have been
identified by other targeted analyses are detected, but no statistically
significant evidence for other gravitational wave bursts is found.
Sensitivities to a variety of signals are presented. These include updated
upper limits on the source rate-density as a function of the characteristic
frequency of the signal, which are roughly an order of magnitude better than
previous upper limits. This search is sensitive to sources radiating as little
as $\sim$10$^{-10} M_{\odot} c^2$ in gravitational waves at $\sim$70 Hz from a
distance of 10~kpc, with 50\% detection efficiency at a false alarm rate of one
per century. The sensitivity of this search to two plausible astrophysical
sources is estimated: neutron star f-modes, which may be excited by pulsar
glitches, as well as selected core-collapse supernova models.
