Planet formation unfolds in environments where stars are rarely alone: the majority of stellar systems are binaries, triples, or higher-order multiples. Hence, stellar multiplicity profoundly shapes the structure, evolution, and dynamics of protoplanetary discs. In this talk, we will explore how discs evolve under the gravitational influence of multiple stars and how this impacts planet formation. I will first summarise recent theoretical and numerical studies on disc dynamics in binary and triple systems, complemented by illustrative examples from observations (e.g. ALMA and VLT) of young multiple stellar systems with discs and planets. Next, I will discuss our modelling efforts within the Stellar-MADE ERC project to investigate accretion, disc morphology, and orbital architecture in these complex systems. Finally, we will highlight the implications for dust evolution, planet formation, and long-term planetary stability.