We present two approaches to solving the airborne electromagnetic (AEM) problems given the induced polarization (IP) effect: with calculating the field in a polarizable medium directly in the time domain (TD) and with calculating the EM+IP field in the frequency domain (FD) followed by a transition to the time domain. The first approach is based on calculating the field at each time step given the sources that depend on the currents excited in the medium at previous time steps. This approach allows us to use any IP decay functions. The frequency domain approach is based on the Fourier series expansion of a non-stationary source and the Cole-Cole model. In order to reduce the computational cost, we use the Hermite spline interpolation. Both approaches allow modeling EM + IP processes in complex media with topography and the curved boundaries of layers containing 3D heterogeneities. 3D modeling is performed on non-conforming hexahedral meshes generated fully automatically. The analysis of computational efficiency and verification of the developed approaches are presented in comparison with the results from other researchers. Moreover, we compare the results obtained in the time and frequency domains. The results of 3D modeling the IP effects, which are obtained for some geoelectrical models typical for AEM exploration problems, are demonstrated.