Electric currents induced in conductive planetary interiors by time-varying magnetospheric and ionospheric current systems have a significant effect on electromagnetic (EM) field observations. Complete characterization of EM induction effects is difficult owing to nonlinear interactions between the three-dimensional electrical structure of a planet and spatial complexity of inducing current systems. We present, a general framework for time-domain modeling of three-dimensional EM induction effects in heterogeneous conducting planets. Our approach does not assume that the magnetic field is potential, allows for an arbitrary distribution of electrical conductivity within a planet, and can deal with spatially complex time-varying current systems. The method is applicable to both data measured at stationary observation sites and satellite platforms, and enables the calculation of three-dimensional EM induction effects in near real-time settings.