Rupture is one of the least investigated and least understood features of the rheological behaviour of polymeric Liquids. Some key experimental results on the rupture of polymer melts in uniaxial extension are discussed. Three features of experimental results for narrow molecular weight distribution (MWD) polymers may be highlighted. Firstly, steady elongational flow becomes impossible and rupture of the liquid filament occurs when and if the stored elastic (Hencky) strain reaches 0.5 units. This can be interpreted in terms of a critical Weissenberg number. Secondly, at higher rates of strain (when the elastic strain becomes more than 0.5) the relationship between limiting stress and elastic strain (at the breaking point) is linear. In this case the limiting elastic strain can become at least as high as 2. Thirdly, the strength of a fluid polymer is not a constant but may be characterised by the lifetime, or durability, t* of the filament. This leads to an empirical criterion for rupture : M = root(sigma(3)t*/eta) = 0.30 +/- 0.05 MJ/m, where eta is the shear viscosity, sigma is the stress at rupture, and M has the dimension of specific energy. This criterion also predicts conditions of rupture for various complicated deformation histories. These results are compared with results for broad MWD polymers. Theoretical criteria based on the results are related to rheological ideas and hypotheses concerning rupture, highlighting areas where further work is required.