  Rapidly decaying long-period oscillations often occur in hot coronal loops of
active regions associated with small (or micro-) flares. This kind of wave
activity was first discovered with the SOHO/SUMER spectrometer from Doppler
velocity measurements of hot emission lines, thus also often called "SUMER"
oscillations. They were mainly interpreted as global (or fundamental mode)
standing slow magnetoacoustic waves. In addition, increasing evidence has
suggested that the decaying harmonic type of pulsations detected in light
curves of solar and stellar flares are likely caused by standing slow-mode
waves. The study of slow magnetoacoustic waves in coronal loops has become a
topic of particular interest in connection with coronal seismology. We review
recent results from SDO/AIA and Hinode/XRT observations that have detected both
standing and reflected intensity oscillations in hot flaring loops showing the
physical properties (e.g., oscillation periods, decay times, and triggers) in
accord with the SUMER oscillations. We also review recent advances in theory
and numerical modeling of slow-mode waves focusing on the wave excitation and
damping mechanisms. MHD simulations in 1D, 2D and 3D have been dedicated to
understanding the physical conditions for the generation of a reflected
propagating or a standing wave by impulsive heating. Various damping mechanisms
and their analysis methods are summarized. Calculations based on linear theory
suggest that the non-ideal MHD effects such as thermal conduction, compressive
viscosity, and optically thin radiation may dominate in damping of slow-mode
waves in coronal loops of different physical conditions. Finally, an overview
is given of several important seismological applications such as determination
of transport coefficients and heating function.
