Quasi-periodic pulsations (or QPPs) are periodic intensity variations in the flare emission, across all wavelength bands. In this paper, we review the observational and modelling achievements since the previous review on this topic by Nakariakov and Melnikov (2009). In recent years, it has become clear that QPPs are an inherent feature of solar flares, because almost all flares exhibit QPPs. Moreover, it is now firmly established that QPPs often show multiple periods. We also review possible mechanisms for generating QPPs. Up to now, it has not been possible to conclusively identify the triggering mechanism or cause of QPPs. The lack of this identification currently hampers possible seismological inferences of flare plasma parameters. QPPs in stellar flares have been detected for a long time, and the high quality data of the Kepler mission allows to study the QPP more systematically. However, it has not been conclusively shown whether the time scales of stellar QPPs are different or the same as those in solar flares.

Space Sci. Rev. manuscript No.

Context. Large-scale fast waves with perturbation of the EUV emission intensity are well resolved in both temporal and spatial scale by SDO/AIA. These waves are prone to propagate along the magnetic field line. Aims. We aim to probe the link between propagating fast wave trains and flaring energy releases. By measuring the wave parameters, we reveal their nature and investigate the potential to diagnose the energy source and waveguide. Methods. The spatial and temporal evolution of the wave amplitude and propagating speed are studied. The correlation of individual wave trains with flare-generated radio bursts is tested. Results. The propagating wave pattern comprises distinct wave trains with varying periods and wavelengths. This characteristic signature is consistent with the patterns formed by waveguide dispersion, when different spectral components propagate at different phase and group speeds. The wave train releases are found to be highly correlated in start time with the radio bursts emitted by the nonthermal electrons that were accelerated in bursty energy releases. The wave amplitude is seen to reach the maximum midway during its course. This can be caused by a combined effect of the waveguide spread in the transverse direction and density stratification. The transverse amplitude distribution perpendicular to the wave vector is found to follow approximately a Gaussian profile. The spatial structure is consistent with the kink mode that is polarised along the line-of-sight. The propagating speed is subject to deceleration from ∼735−845 km s −1 to ∼600 km s −1 . This could be caused by the decrease in the local Alfvén speed and/or the projection effect.