An electronic device may have a display with touch sensors. One or more shielding layers may be interposed between the display and the touch sensors. The shielding layers may include shielding structures such as a conductive mesh structure and/or a transparent conductive film. The shielding structures may be actively driven or passively biased. In the active driving scheme, one or more inverting circuits may receive a noise signal from a cathode layer in the display and/or from the shielding structures, invert the received noise signal, and drive the inverted noise signal back onto the shielding structures to prevent any noise from the display from negatively impacting the performance of the touch sensors. In the passive biasing scheme, the shielding structures may be biased to a power supply voltage.