Long neglected by research on specialized languages, diachronic approaches currently seem to experience their coming of age. However, studies on diachronic aspects of LSPs still show significant heterogeneity, both in objectives and methods. This may reflect their high investigative potential, but also supports the view that, while it is no longer necessary to make a plea for diachronic approaches, the ways in which they can be applied to LSPs warrant further investigation. We propose to adopt the angle of textual terminology to evaluate their applications in LSPs, as, for several years now, this approach has sought to build a systematic framework for tool-assisted methods aimed at analysing variations in specialized corpora, and has endeavored to establish their theoretical tenets, by factoring in actual contexts of use. In particular, textual terminology has questioned the validity of several "pillars" of diachronic studies, discussing such notions as "corpora", "tools", "experts", and "interpretation".