Two major movements are actively at work to change the way research is done, shared, and reproduced. The first is the reproducible research (RR) approach, which has never been easier to implement given the current availability of tools and DIY manuals. The second is the FAIR (Findable, Accessible, Interoperable, and Reusable) approach, which aims to support the availability and sharing of research materials. We show here that despite the efforts made by researchers to improve the reproducibility of their research, the initial goals of RR remain mostly unmet. There is great demand, both within the scientific community and from the general public, for greater transparency and for trusted published results. As a scientific community, we need to reorganize the diffusion of all materials used in a study and to rethink the publication process. Researchers and journal reviewers should be able to easily use research materials for reproducibility, replicability, or reusability purposes or for exploration of new research paths. Here we present how the research process, from data collection to paper publication, could be reorganized and introduce some already available tools and initiatives. We show that even in cases in which data are confidential, journals and institutions can organize and promote “FAIR-like RR” solutions where not only the published paper but also all related materials can be used by any researcher.