The numbers were assigned by Wolfgang Schmieder in 1950, indicating the placement in the catalogue of Bach's works entitled Thematisch-Systemattisches Verzeichnis der musikalischen Werke von Johann Sebastian Bach. The BWV numbers are universally used and accepted as the standard way of numbering the works of Bach, for example: "Mass in B minor, BWV 232, composed in 1733". At times the BWV numbers are called Schmieder numbers - the terms are interchangeable.
Unlike some other catalogues which are arranged chronologically, Schmieder's is arranged by type of work, so that choral works come first, then works for organ, then other keyboard works, and so on. For this reason, a low BWV number does not necessarily indicate an early work.
For a list of Bach's works arranged by BWV number, see list of compositions of Johann Sebastian Bach.