We analyse the quenched fractions, gas content, and star formation histories of ∼1200 satellite galaxies with 𝑀 * ≥ 5 × 10 6 M around 198 Milky Way-(MW) and Andromeda-like (M31) hosts in TNG50, the highest-resolution run of the IllustrisTNG simulations. Satellites exhibit larger quenched fractions for smaller masses, at smaller distances to their host galaxy, and in the more massive M31-like compared to MW-like hosts. As satellites cross their host's virial radius, their gas content drops significantly: most satellites within 300 kpc do not contain any detectable gas reservoirs at 𝑧 = 0, unless they are massive like the Magellanic Clouds and M32. Nevertheless, their stellar assembly exhibits a large degree of diversity. On average, the cumulative star formation histories of satellites are more extended for brighter, more massive satellites with a later infall, and for those in less massive hosts. Based on these relationships, we can even infer infall periods for observed MW and M31 dwarfs: e.g. 0 − 4 Gyr ago for the Magellanic Clouds and Leo I, 4 − 8 and 0 − 2 Gyr ago for M32 and IC 10, respectively. Ram pressure stripping (in combination with tidal stripping) deprives TNG50 satellites of their gas reservoirs and ultimately quenches their star formation activity, even though only a few per cent of the present-day satellites around the 198 TNG50 MW/M31-like hosts appear as jellyfish. The typical time since quenching for currently quenched TNG50 satellites is 6.9 +2.5 −3.3 Gyr ago. The TNG50 results are consistent with the quenched fractions and stellar assembly of observed MW and M31 satellites, however, satellites of the SAGA survey exhibit lower quenched fractions than TNG50 and other, observed analogues.