Binaries sufficiently compact to be observed with LISA consist of small stars, with both chosen from the following list: low-mass main sequence stars, white dwarfs, neutron stars, black holes or helium-burning cores of high-mass stars. The numbers of various types of binaries can be derived from observations, provided that observational selection effects are taken into account. They can also be derived from theoretical population synthesis, but the uncertainties are such that the resulting numbers must be gauged with observed samples.