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The ninth edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2021) was organized to take place on 13–16 June 2021. Due to the pandemic, COUPLED 2021 was a fully online and completely synchronous conference. The previous eight editions of this conference were held on the islands of Santorini (Greece) on 25-28 May 2005; Ibiza (Spain) on 21–23 May 2007; Ischia (Italy) on 8–11 June 2009; Kos (Greece) on 20–22 June 2011; Ibiza (Spain) on 17–19 June 2013; San Servolo, Venice (Italy), on 18–20 May 2015; Rhodes Island (Greece) on 12–14 June 2017; and Sitges (Spain) on 3–5 June 2019. The objectives of COUPLED PROBLEMS 2021 were to present and discuss the state of the art in mathematical models, numerical methods and computational techniques for solving coupling problems of a multidisciplinary character in science and engineering. The conference’s goal was to make advances in the formulation and solution of real-life problems with a multidisciplinary perspective, accounting for all the complex couplings involved in the physical description of the problem. The conference was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS) and a Special Interest Conference of the International Association for Computational Mechanics (IACM). It was also supported by other scientific organizations in Europe and across the globe.