Summary figure of CAVITY and project extension. This figure is divided into three main sections. At the top we illustrate some randomly selected CAVITY voids within the large-scale structure of the Universe (as a wedge plot on the left, Argudo-Fernández et al. 2017) and show the spatial distribution of galaxies within a typical void (void 486; each dot corresponds to a different galaxy colour-coded by redshift). The webs of colour lines link galaxy members and depict the location of each highlighted void. The middle right panel (framed by a grey square) zooms in on CAVITY62480, an example galaxy contained in void 482, showing its SDSS colour image with the PMAS footprint (green hexagon), INT cutout (blue square), and IRAM beam (purple circle) on top of it. The next main section (framed by the green rectangle) is devoted to illustrate the IFS data. We represent the integrated light of the galaxy within the covered wavelength range of the instrument (on top), the spectrum of the central spaxel (in the middle), and the gas velocity and stellar age maps (at the bottom) as examples of the potential of IFS data in deriving spatially resolved distributions of the galaxy properties. The third and final section is devoted to CAVITY+, the complementary observational campaigns that shape the CAVITY project extension. Here we show a coloured image using the INT g- and r-band deep imaging (framed by the blue rectangle, bottom middle panel) and the integrated CO(1–0) spectrum from the IRAM observations (purple rectangle, bottom right panel) for CAVITY62480.