Hyperspectral imaging generates data volumes of unprecedented scale and complexity, requiring methodological advances that fully harness the richness of the captured information. This chapter delves into the fast proliferation of hyperspectral data and the increased complexity introduced by the integration of multiple modalities, which collectively impose considerable computational and storage demands when processing hundreds of spectral bands. To mitigate these requirements, advanced techniques for scalable storage and distributed processing are evaluated. Particular emphasis is placed on cutting-edge processing paradigms, analyzing approaches that range from lightweight on-board systems that mitigate downlink bottlenecks to cloud computing (CC) solutions. In particular, CC provides elastic resource allocation, near-unlimited storage capacity, and high availability, providing a scalable platform for the optimal deployment of computationally intensive algorithms. Building on these advantages, the chapter provides a comprehensive review of the state-of-the-art algorithms executed on distributed frameworks such as Apache Hadoop and Apache Spark. The discussion culminates in a real case study focused on marine oil-spill detection to determine the performance of Apache Hadoop and Elastic MapReduce over a CC environment using PRISMA imagery. These insights establish a clear roadmap for exploiting large hyperspectral datasets within high-performance computing environments, enabling rapid and efficient data processing.