We analyse the properties of strongly-barred disc galaxies using the TNG100 simulation, a cosmological hydrodynamical realisation of the IllustrisTNG suite. We identify 270 disc galaxies at z = 0 in the stellar mass range M * = 10 10.4−11 M , of which 40 per cent are barred. Of the detected bars, more than half are strong. We find that the fraction of barred galaxies increases with stellar mass, in agreement with observational results. Strongly-barred galaxies present, overall, lower gas-to-stellar mass ratio compared to unbarred galaxies. The majority of barred galaxies are quenched (sSFR ∼ 10 −11.7 yr −1 ), whereas unbarred galaxies continue to be active (sSFR ∼ 10 −10.3 yr −1 ) in the main sequence of the star-forming galaxies. We explore the evolution of stronglybarred and unbarred galaxies to investigate their formation and quenching history. We find that strong bars form between 0.5 < z < 1.5, with more massive galaxies hosting older bars. Strong bars form in galaxies with an early-established prominent disc component, undergoing periods of enhanced SFR and black hole accretion, possibly assisted by cosmological inflows. Unbarred galaxies, instead, assemble most of their mass and disc component at late times. The nuclear region of strongly-barred galaxies quenches shortly after bar formation, while unbarred galaxies remain active across time. Our findings are indicative of bar quenching, possibly assisted by nuclear feedback processes. We conclude that the cosmological environment, together with small scale feedback processes, determine the chances of a galaxy to form a bar and to rapidly quench its central region.