Physics-Informed Neural Networks (PINNs) are fast becoming an important tool to solve differential equations rapidly and accurately, and to identify the systems parameters that best agree with a given set of measurements. PINNs have been used for cardiac electrophysiology (EP), but only in simple 1D and 2D geometries and for sinus rhythm or single rotor dynamics. Here, we demonstrate how PINNs can be used to accurately reconstruct the propagation of cardiac action potentials in more complex geometries and dynamical regimes. These include 3D spherical geometries and spiral break-up conditions that model cardiac fibrillation, with a mean RMSE \(< 5.1\times 10^{-2}\) overall. We also demonstrate that PINNs can be used to reliably parameterise cardiac EP models with some biological detail. We estimate the diffusion coefficient and parameters related to ion channel conductances in the Fenton-Karma model in a 2D setup, achieving a mean relative error of \(-0.09\pm 0.33\) . Our results are an important step towards the deployment of PINNs to realistic cardiac geometries and arrhythmic conditions.