In multiple stellar systems, interactions among the companion stars and their discs affect planet formation. In the circumstellar case, tidal truncation makes protoplanetary discs smaller, fainter and less long-lived than those evolving in isolation, thereby reducing the amount of material (gas and dust) available to assemble planetary embryos. On the contrary, in the circumbinary case the reduced accretion can increase the disc lifetime, with beneficial effects on planet formation. In this chapter we review the main observational results on discs in multiple stellar systems and discuss their possible explanations, focusing on recent numerical simulations, mainly dealing with dust dynamics and disc evolution. Finally, some open issues and future research directions are examined.