[en] We propose that the concept of liquids characterized by a given locally preferred structure (LPS) could help in understanding the observed phenomenon of polyamorphism. 'True polyamorphism' would involve the competition between two (or more) distinct LPSs, one favoured at low pressure because of its low energy and one favoured at high pressure because of its small specific volume, as in tetrahedrally coordinated systems. 'Apparent polyamorphism' could be associated with the existence of a poorly crystallized defect-ordered phase with a large unit cell and small crystallites, which may be illustrated by the metastable glacial phase of the fragile glass-former triphenylphosphite; the apparent polyamorphism might result from structural frustration, i.e., a competition between the tendency to extend the LPS and a global constraint that prevents tiling of the whole space by the LPS