<p>Ohm’s law has been a cornerstone of electronics since its experimental discovery. This law establishes that, in a conductive system, the voltage is directly proportional to the current. Even when time-reversal symmetry is disrupted, leading to the emergence of magnetoresistance and Hall effects, the linear relationship between voltage and current remains intact. However, recent experiments have demonstrated a breakdown of Ohm’s law in non-centrosymmetric structures. In these systems, nonlinear transport effects are permitted with quadratic scaling between voltages and currents. Here we review the main demonstrations of nonlinear transport in non-centrosymmetric systems, analysing the connection between nonlinear behaviour and the system’s symmetry. We also investigate the microscopic mechanisms driving these effects, such as Berry curvature dipole and Berry connection polarizability. Finally, we highlight potential applications of nonlinear transport in spintronics and energy harvesting.</p>