We use cosmological simulations to study a characteristic evolution pattern of high-redshift galaxies. Early, stream-fed, highly perturbed, gas-rich discs undergo phases of dissipative contraction into compact, star-forming systems (‘blue’ nuggets) at z ∼ 4–2. The peak of gas compaction marks the onset of central gas depletion and inside-out quenching into compact ellipticals (red nuggets) by z ∼ 2. These are sometimes surrounded by gas rings or grow extended dry stellar envelopes. The compaction occurs at a roughly constant specific star formation rate (SFR), and the quenching occurs at a constant stellar surface density within the inner kpc (Σ1). Massive galaxies quench earlier, faster, and at a higher Σ1 than lower mass galaxies, which compactify and attempt to quench more than once. This evolution pattern is consistent with the way galaxies populate the SFR-size–mass space, and with gradients and scatter across the main sequence. The compaction is triggered by an intense inflow episode, involving (mostly minor) mergers, counter-rotating streams or recycled gas, and is commonly associated with violent disc instability. The contraction is dissipative, with the inflow rate >SFR, and the maximum Σ1 anticorrelated with the initial spin parameter. The central quenching is triggered by the high SFR and stellar/supernova feedback (maybe also active galactic nucleus feedback) due to the high central gas density, while the central inflow weakens as the disc vanishes. Suppression of fresh gas supply by a hot halo allows the long-term maintenance of quenching once above a threshold halo mass, inducing the quenching downsizing.