The quadrupole ion trap is widely used in the chemical physics community for making measurements on dynamical systems, both intramolecular (e.g. ion fragmentation reactions) and intermolecular (e.g. ion/molecule reactions). In this review, we discuss linear and nonlinear resonances in quadrupole ion traps, an understanding of which is critical for operation of these devices and interpretation of the data which they provide. The effect of quadrupole field nonlinearity is addressed, with important implications for promoting fragmentation and achieving unique methods of mass scanning. Methods that depend on ion resonances (i.e. matching an external perturbation with an ion's induced frequency of motion) are discussed, including ion isolation, ion activation, and ion ejection. (C) 2016 Elsevier B.V. All rights reserved.