This article describes recent progress on premixed flame dynamics interacting with acoustic waves. Expressions are derived to determine the stability of combustors with respect to thermoacoustic oscillations. The validity of these expressions is general, but they are illustrated in laminar systems. Laminar burners are commonly used to elucidate the response of premixed flames to incoming flow perturbations, highlight the role of acoustic radiation in their stability, identify modes associated with thermoacoustic intrinsic instabilities and decipher the leading mechanisms in annular systems with multiple injectors. Many industrial devices also operate in a laminar premixed mode such as, for example, domestic gas boilers and heaters equipped with matrix burners for material processing in which unconfined flames are stabilized at one extremity of the system. This article proposes a systematic approach to determine the stability of all these systems with respect to thermoacoustic oscillations by highlighting the key role of the burner impedance and the flame transfer function (FTF). This transfer function links in frequency space incoming flow perturbations to heat release rate disturbances. This concept can be used in the turbulent flame case as well. Weakly nonlinear stability analysis can also easily be conducted by replacing the FTF by a flame describing function in the expressions derived in this work. The response of premixed flames to harmonic mixture compositions and flow-rate perturbations is then revisited and the main parameters controlling the FTF are described. A theoretical framework is finally developed to reduce the system thermoacoustic sensitivity by tailoring the FTF.