Context. About a third of the hot subdwarfs of spectral type B (sdBs), which are mostly core-helium-burning objects on the extreme horizontal branch, are found in close binaries with cool, low-mass stellar, substellar, or white dwarf companions. They can show light variations due to different phenomena. Aims. Many hot subdwarfs now have space-based light curves with a high signal-to-noise ratio available. We used light curves from the Transiting Exoplanet Survey Satellite and the K2 space mission to look for more sdB binaries. Their light curves can be used to study the hot subdwarf primaries and their companions, and obtained orbital, atmospheric, and absolute parameters for those systems, when combined with other analysis methods. Methods. By classifying the light variations and combining these with the fit of the spectral energy distribution, the distance derived by the parallaxes obtained by Gaia, and the atmospheric parameters, mainly from the literature, we could derive the nature of the primaries and secondaries in 122 (75%) of the known sdB binaries and 82 newly found reflection effect systems. We derived absolute masses, radii, and luminosities for a total of 39 hot subdwarfs with cool, low-mass companions, as well 29 known and newly found sdBs with white dwarf companions. Results. The mass distribution of hot subdwarfs with cool, low-mass stellar and substellar companions, differs from those with white dwarf companions, implying they come from different populations. By comparing the period and minimum companion mass distributions, we find that the reflection effect systems all have M dwarf or brown dwarf companions, and that there seem to be several different populations of hot subdwarfs with white dwarf binaries – one with white dwarf minimum masses around 0.4 M⊙, one with longer periods and minimum companion masses up to 0.6 M⊙, and at the shortest period, another with white dwarf minimum masses around 0.8 M⊙. We also derive the first orbital period distribution for hot subdwarfs with cool, low-mass stellar or substellar systems selected from light variations instead of radial velocity variations. It shows a narrower period distribution, from 1.5 h to 35 h, compared to the distribution of hot subdwarfs with white dwarfs, which ranges from 1 h to 30 days. These period distributions can be used to constrain the previous common-envelope phase.