A rigorous mathematical framework for studying the nonlinear dynamics of charged drops has been developed and summarized here. A combination of domain perturbation and multiple timescale methods are systematically used to compute the evolution of axisymmetric, inviscid and charged drops that exhibit a number of nonlinear phenomena.Nuclear physics has contributed theoretical analysis and impetus for experimental study of liquid drops, since Bohr and Wheeler began modeling atomic nuclei as uniformly charged liquid drops with surface tension. When moderate amplitude oscillations of charged drops are considered, it is shown that the increased inertia of the system slows down the motion by decreasing the frequency of the oscillation. The analysis also demonstrates the possibility of resonance between the fundamental mode of oscillation and one of its harmonics for particular values of the net charge on the drop. Both frequency and amplitude modulation of the oscillations are predicted for drop motions starting from general initial conditions. This effect cannot be anticipated from the linear analysis and proves that Rayleigh’s solution for small‐amplitude oscillations can actually be unstable.The dynamics of break‐up of a charged drop is a long standing issue, although the neutrally stable states have been known since the early sixties. Rayleigh calculated the maximum charge that a spherical drop can carry before it becomes unstable due to electrostatic repulsion. The present analysis shows that the first axisymmetric family that bifurcates from the spherical shape evolves transcritically, so that the drop will be either unstable for elongated prolate shapes or stable for flat oblate shapes. The evolution of drop shapes leading to break‐up is also analyzed, and the dependence of the amount of charge on the amplitude of the deformations is computed. The asymptotic analysis for the static shapes is in very good agreement with the finite element calculations for even large amplitude deformations for the drop. Recently, it has been shown that oblate spheroids are unstable with respect to non‐axisymmetric disturbances and, thus, are not observable.