Plasmas permeate our Universe, being present in stellar atmospheres, interstellar gas clouds in galaxies, planetary nebulae, supernova remnants, black hole accretion disks, and so on. Spectroscopy of all these objects has shown a richness of information, in particular in the spectral lines that are emitted by the ions that are present in the plasmas. In recent years, an overwhelming amount of XUV spectroscopic data have been obtained from missions such as Chandra, XMM-Newton, HST, FUSE, SOHO. The state of matter in each object --- the distribution of temperature and density, chemical composition, flow velocities --- can be determined through diagnostic analysis of spectral data in which models, incorporating the full physics of the object, confront the observations. This information is fundamental for our understanding of the origin and evolution of the Universe. Collisions of electrons and photons with atoms, ions and molecules play a fundamental role in astrophysical plasmas, and it is therefore necessary that accurate atomic data are calculated. It might be surprising, but a large fraction of the spectra produced by ions is still unexplored. Large discrepancies between observations and theory are also still present. For example, there are order-of-magnitude anomalies in the derived elemental abundances in H II regions and Planetary Nebulae. A mis-match between observation and theory is also present in the X-ray spectra of Active Galactic Nuclei (AGN). We intend to perform new calculations of electron-ion recombination rate coefficients to address these discrepancies. In recent years, we have shown the need to perform accurate R-matrix calculations of electron-ion collisions for individual ions, in order to solve the large, long-standing discrepancies between observed and calculated line intensities in collisional (astrophysical and laboratory) plasmas. We propose extending these calculations to all isolectronic sequences from H-like up to Na-like, providing a comprehensive and accurate dataset for all important ions. The theoretical data need to be assessed and benchmarked against astrophysical and laboratory measurements, in particular, in order to identify spectral lines and to provide accurate wavelengths and uncertainty estimates. We intend to provide all of these fundamental and derived data to the wider user community by setting up a web-based archive which will contain all of the atomic data needed to interpret, with physical modelling, the spectra of astrophysical and laboratory plasmas. With this proposal, we aim to strengthen the collaboration between experimental, observational and theoretical research.