This paper reviews current understanding of the manner in which non-premixed jet flames respond to flow disturbances, and compares these characteristics to premixed flames. Disturbances in flow velocity excite wrinkles on non-premixed flame sheets and perturbations in heat release. These disturbances convect axially along the flame at the local flow velocity and decay in amplitude. Sufficiently large disturbance amplitudes cause opposing sides of the flame to merge and pinch off, leading to multiply connected flame sheets. The space-time characteristics of flame wrinkles on premixed and non-premixed flame sheets are quite similar, as they are dominated by flow disturbances moving the flame around, convection of the wrinkles downstream, and dissipation of wrinkles. In contrast, the heat release dynamics are quite different, as heat release oscillations in premixed flames are nearly uniformly distributed along the flame, whereas in non-premixed flames they are concentrated near the burner outlet where mixture fraction gradients are highest. In addition, flame area fluctuations are the dominant mechanism leading to heat release oscillations in constant burning velocity premixed flames, while mass burning rate oscillations dominate non-premixed flames. The flame transfer function, i.e., the normalized ratio of heat release and flow oscillations, is of O(1) at low frequencies and transitions to a 1/St behavior at high frequencies, for both premixed and non-premixed flames, where St denotes the flame Strouhal number, physically representing the ratio of the convective and the forcing time-scale. While the mechanisms dominating heat release oscillations are quite different for premixed and non-premixed flames, these comparable asymptotic tendencies are actually the result of the same effects: namely, that the heat release is proportional to the instantaneous mass flux of reactants in the quasi-steady, low Strouhal number case, and phase cancellation associated with convecting regions of oscillatory heat release leads to the 1/St behavior in the St >> 1 regime. Non-premixed flames have an additional 1/root st transfer function character at an intermediate range of Strouhal numbers, due to the sharply varying axial dependence of mean heat release near the burner exit. (C) 2018 Elsevier Ltd. All rights reserved.