In my talk, I shall review the main research projects I'm involved in, which all revolve around the added value of cross-correlations between various cosmological observables, as well as among cosmological and astrophysical observables, to shed new light onto pressing open questions in cosmology. In particular, I shall touch upon the possibility of detecting relativistic effects on cosmological scales - which will allow us to deepen our understanding of dark energy and modified gravity -, novel approaches to probe primordial non-Gaussianity, and the use of cosmological data to filter out astrophysical processes in studies of indirect detection of particle dark matter signatures. All this in the view of the new generation of cosmological experiments across the electromagnetic spectrum, like the SKA Observatory in the radio band, or the Euclid satellite at optical/near-infrared wavelengths.