Often the enhanced electromagnetic radiation generated in solar and stellar flares shows a pronounced (quasi)-oscillatory pattern—quasi-periodic pulsations (QPP), with characteristic periods ranging from a fraction of a second to several tens of minutes. We review recent advances in the empirical study of QPP in solar and stellar flares, addressing the intrinsic non-stationarity of the signal, i.e. the variation of its amplitude, period or phase with time. This non-stationarity could form a basis for a classification of QPP, necessary for revealing specific physical mechanisms responsible for their appearance. We could identify two possible classes of QPP, decaying harmonic oscillations, and trains of symmetric triangular pulsations. Apparent similarities between QPP and irregular geomagnetic pulsations Pi offer a promising avenue for the knowledge transfer in both analytical techniques and theory. Attention is also paid to the effect of the flare trend on the detection and analysis of QPP.