  Magnetic storms on stars manifest as remarkable, randomly occurring changes
of the luminosity over durations that are tiny in comparison to the normal
evolution of stars. These stellar flares are bursts of electromagnetic
radiation from X-ray to radio wavelengths, and they occur on most stars with
outer convection zones. They are analogous to the events on the Sun known as
solar flares, which impact our everyday life and modern technological society.
Stellar flares, however, can attain much greater energies than those on the
Sun. Despite this, we think that these phenomena are rather similar in origin
to solar flares, which result from a catastrophic conversion of latent magnetic
field energy into atmospheric heating within a region that is relatively small
in comparison to normal stellar sizes. We review the last several decades of
stellar flare research. We summarize multi-wavelength observational results and
the associated thermal and nonthermal processes in flaring stellar atmospheres.
Static and hydrodynamic models are reviewed with an emphasis on recent progress
in radiation-hydrodynamics and the physical diagnostics in flare spectra.
Thanks to their effects on the space weather of exoplanetary systems (and thus
in our search for life elsewhere in the universe) and their preponderance in
\emph{Kepler} mission data, white-light stellar flares have re-emerged in the
last decade as a widely-impactful area of study within astrophysics. Yet, there
is still much we do not understand, both empirically and theoretically, about
the spectrum of flare radiation, its origin, and its time evolution. We
conclude with several big-picture questions that are fundamental in our pursuit
toward a greater understanding of these enigmatic stellar phonemena and, by
extension, those on the Sun.
