Materials Cloud is a platform designed to enable open and seamless sharing of resources for computational science, driven by applications in materials modelling. It hosts (1) archival and dissemination services for raw and curated data, together with their provenance graph, (2) modelling services and virtual machines, (3) tools for data analytics, and pre-/post-processing, and (4) educational materials. Data is citable and archived persistently, providing a comprehensive embodiment of entire simulation pipelines (calculations performed, codes used, data generated) in the form of graphs that allow retracing and reproducing any computed result. When an AiiDA database is shared on Materials Cloud, peers can browse the interconnected record of simulations, download individual files or the full database, and start their research from the results of the original authors. The infrastructure is agnostic to the specific simulation codes used and can support diverse applications in computational science that transcend its initial materials domain.