Rechargeable potassium-ion batteries (PIBs) are of great interest as a sustainable, environmentally friendly, and cost-effective energy storage technology. The electrochemical performance of a PIB is closely related to the reaction kinetics of active materials, ionic/electronic transport, and the structural/electrochemical stability of cell components. Alongside the great effort devoted in discovering and optimising electrode materials, recent research unambiguously demonstrates the decisive role of the interphases that interconnect adjacent components in a PIB. Knowledge of interphases is currently less comprehensive and satisfactory compared to that of electrode materials, and therefore, understanding the interphases is crucial to facilitate electrode materials design and advance battery performance. The present review aims to summarise the critical interphases that dominate the overall battery performance of PIBs, which includes solid-electrolyte interphase (SEI), cathode-electrolyte interphase (CEI), and solid-solid interphases in composite electrodes, via exploring their formation principles, chemical compositions, and determination of reaction kinetics. State-of-the-art design strategies of robust interphases are discussed and analysed. Finally, perspectives are given to stimulate new ideas and open questions to further the understanding of interphases and the development of PIBs.