In many continuous combustion processes the flame is stabilized by swirling the injected flow. This is the case for example in aeroengine combustors or in gas turbines where aerodynamic injectors impart a rotating component to the flow to create a central recirculation zone which anchors the flame. Swirling flame dynamics is of technical interest and also gives rise to interesting scientific issues. Some of the recent progress in this field will be reviewed. It is first shown that the swirler response to incident acoustic perturbations generates a vorticity wave which is convected by the flow. A result of this process is that the swirl number fluctuates. It is then shown that the flame response is defined by a combination of heat release rate fluctuations induced by the incoming acoustic and convective perturbations. This is confirmed by experimental measurements and by large eddy simulations of the reactive flow. Measured flame describing functions (FDFs) are then used to characterize the nonlinear response of swirling flames to incident perturbations and determine the regimes of instability of a generic system comprising an upstream manifold, an injector equipped with a swirler and a combustion chamber confining the flame. The last part of this article is concerned with interactions of the precessing vortex core (PVC) with incoming acoustic perturbations. The PVC is formed at high swirl number and this hydrodynamic helical instability gives rise to some interesting nonlinear interactions between the acoustic frequency, the PVC frequency and their difference frequency.