Approximately 70 per cent of the nearby white dwarfs appear to be single stars, with the remainder being members of binary or multiple star systems. The most numerous and most easily identifiable systems are those in which the main-sequence companion is an M star, since even if the systems are unresolved the white dwarf either dominates or is at least competitive with the luminosity of the companion at optical wavelengths. Harder to identify are systems where the non-degenerate component has a spectral type earlier than M0 and the white dwarf becomes the less luminous component. Taking Sirius as the prototype, these latter systems are referred to here as 'Sirius like'. There are currently 98 known Sirius-like systems. Studies of the local white dwarf population within 20 pc indicate that approximately 8 per cent of all white dwarfs are members of Sirius-like systems, yet beyond 20 pc the frequency of known Sirius-like systems declines to between 1 and 2 per cent, indicating that many more of these systems remain to be found. Estimates are provided for the local space density of Sirius-like systems and their relative frequency among both the local white dwarf population and the local population of A to K main-sequence stars. The great majority of currently unidentified Sirius-like systems will likely turn out to be closely separated and unresolved binaries. Ways to observationally detect and study these systems are discussed.