A brief critical review is given of diverse techniques used to measure heterojunction band lineups; they range from very reliable to worthless. Another problem pertains to the heterosystems themselves: Data on systems in which two semiconductors from a different pair of columns of the periodic table are combined, should be reviewed with suspicion, although some selected pairs are probably trustworthy—but none in which a compound semiconductor was grown on an elemental one. Technologies that do not lead to device‐quality interfaces also probably do not yield device‐quality lineup data. A list of the most trustworthy experimental data is given. The simplest possible theoretical framework for a theory of band lineups is a model of linear superpositon of atomiclike bulk potentials. Such a model automatically leads to a theory that is linear and transitive, in which the band lineups are orientation independent, and in which a technology dependence of the band lineups requires a technology‐dependent deviation of the atomic arrangement from the ideal one. The Harrison theory is both the simplest and the most successful theory of band lineups, although it still does not meet the needs of the device physicist. The set of most reliable data selected earlier agree very well with this theory, with a largest deviation of 0.18 eV and a standard deviation of 0.13 eV.