Recent progress made in the prediction, characterisation, and mitigation of multipactor discharge is reviewed for single‐ and two‐surface geometries. First, an overview of basic concepts including secondary electron emission, electron kinetics under the force law, multipactor susceptibility, and saturation mechanisms is provided, followed by a discussion on multipactor mitigation strategies. These strategies are categorised into two broad areas – mitigation by engineered devices and engineered radio frequency (rf) fields. Each approach is useful in different applications. Recent advances in multipactor physics and engineering during the past decade, such as novel multipactor prediction methods, understanding space charge effects, schemes for controlling multipacting particle trajectories, frequency domain analysis, high frequency effects, and impact on rf signal quality are presented. In addition to vacuum electron multipaction, multipactor‐induced ionization breakdown is also reviewed, and the recent advances are summarised.