Oscillations or quasi-periodic pulsations (QPP) are a common feature of the light curves generated by solar and stellar flares. The observed periods range from sub-second to several minutes. Mechanisms for the generation of QPP in microwave, X-ray and visible light emission, based upon magnetohydrodynamic (MHD) oscillations, are discussed. QPP can be produced by internal MHD oscillations of flaring magnetic structures, in particular by kink, sausage and longitudinal modes. Different modes have different observational signatures in different emission bands, allowing for the correct identification of the mode. Another mechanism is based upon periodic triggering of flaring energy releases by oscillations in a non-flaring loop situated nearby the flaring region. The use of observable parameters of QPP for remote diagnostics of coronal plasmas, in particular of the magnetic field in the flaring regions is demonstrated.