Many scientific simulations, machine/deep learning applications and instruments are in need of significant data reduction. Errorbounded lossy compression has been identified as one solution and has been tested for many use-cases: Reducing streaming intensity (instruments), reducing storage and memory footprints, accelerating computation and accelerating data access and transfer. Ultimately, users’ trust in lossy compression relies on the preservation of science: same conclusions should be drawn from computations or analysis done from lossy compressed data. Experience from scientific simulations, Artificial Intelligence (AI) and instruments reveals several points: (i) there are important gaps in the understanding of the effects of lossy compressed data on computations, AI and analysis, (ii) each use-case, application and user has its own requirements in terms of compression ratio, speed and accuracy, and current generic monolithic compressors are not responding well to this need for specialization. This situation calls for more research and development on the lossy compression technologies. This paper addresses the most pressing research needs regarding the application of lossy compression in the scientific context.