The first aim of this review is to assess the experimental data available about surface phase transitions at the contact between fluid bulk phases and either their vapour in the case of liquids (free interfaces) or solid substrates in general and to test their "universal" behaviour out of any consideration about critical laws, which constitute a topic by themselves. As, here, the level under consideration is only the microscopic one, wetting transitions are excluded. Our second goal is to compare these experimental data to their description by models, which are far more numerous. This imposed us to privilege, here, Cahn's and DFT theories because their way of reasoning is very close to classical thermodynamics and so, the discussion of the experimental data under examination here is facilitated with no exclusion of decisive contribution by other kinds of theories. A thorough analysis of available experiments and theoretic works makes layering appear as a general and non-wetting-dependent phenomenon exhibited by simple gases or gas mixtures on solids and also by liquid mixtures. On the other hand, though prewetting is not deeply different in essence, it is fully wetting-dependent. Both phenomena can be found in systems where interactions are very different by nature and, according to very recent models and experiments, the interplay between these interactions may lead to intertwining between both surface phenomena.