About 35 years ago a class of galaxies with unusually strong Balmer absorption lines and weak emission lines was discovered in distant galaxy clusters 1,2 . These objects, alternatively referred to as post-starburst, E+A or k+a galaxies, are now known to occur in all environments and at all redshifts 3–7 , with many exhibiting compact morphologies and low-surface brightness features indicative of past galaxy mergers 3,8 . They are commonly thought to represent galaxies that are transitioning from blue to red sequence, making them critical to our understanding of the origins of galaxy bimodality 9–14 . However, recent observational studies have questioned this simple interpretation 15–18 . From observations alone, it is challenging to disentangle the different mechanisms that lead to the quenching of star formation in galaxies. Here we present examples of three different evolutionary pathways that lead to galaxies with strong Balmer absorption lines in the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulation 19,20 : classical blue → red quenching, blue → blue cycle and red → red rejuvenation. The first two are found in both post-starburst galaxies and galaxies with truncated star formation. Each pathway is consistent with scenarios hypothesized for observational samples 2,15,18,21,22 . The fact that ‘post-starburst’ signatures can be attained via various evolutionary channels explains the diversity of observed properties, and lends support to the idea that slower quenching channels are important at low redshift 23,24 .