It is commonly assumed that hydrostatic pressure balance arguments can be used to establish a relationship between the maximum height to which a volcanic edifice is able to grow and the depth at which the partial melts providing its magma supply are formed. Such a relationship has been used to infer various aspects of the thermal and stress state of the lithosphere beneath volcanic constructs on Earth, Mars, Io and Venus. We examine the assumptions behind this relationship (which are that: (1) a continuous pressure connection exists between source and summit, (2) the pressure around the magma source is the local hydrostatic pressure dictated by the depth below the geoid, and (3) the melt erupting at the summit has a net positive buoyancy), and show that many of them require geologically unreasonable conditions. We then critically assess the evidence cited in the literature for the relationship and find that there are other factors that may explain the observations. We conclude that volcano heights on the terrestrial planets cannot be related in any simple way to lithospheric thickness or depth to the magma source zone and we review the range of other factors controlling volcano height.