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The ATLAS Spanish Tier-1 and Tier-2s have more than 18 years of experience in the deployment and development of LHC computing components and their successful operation. The sites are actively participating in, and in some cases coordinating, R&D computing activities in the LHC Run 3 and developing the computing models needed in the HL-LHC period. In this contribution, we present details on the integration of some components, such as HPC computing resources to execute ATLAS simulation workflows; the development of new techniques to improve efficiency in a cost-effective way; and improvements in Data Organization, Management and Access through storage consolidations, the use of data caches, and improving experiment data catalogues, through contributions such as Event Index. The design and deployment of novel analysis facilities using GPUs together with CPUs and techniques like Machine Learning are also presented. ATLAS Tier-1 and Tier-2 sites in Spain, are, and will be, contributing to significant R&D in computing and evaluating different models for improving performance of computing and data storage capacity in the LHC High Luminosity era.