This article describes a research study concerning students' conceptions and reasonings about fluids and pressure in static situations. After a preliminary survey involving interviews and observations in class, some written questions were answered by various groups, totalling 428 Italian and French pupils in upper secondary school, 458 first-year university students in Belgium and 58 teachers-in-training. After briefly illustrating some results from previous research on this topic, the article introduces the guidelines and objectives of the current research, describes and discusses its results, highlighting some categories of the more diffuse conceptions and tendencies of reasoning, and supplies a few suggestions for teaching. It is shown, among other things, that the notion of hydrostatic pressure is strongly connected to the idea of weight and associated with all the ambiguities that usually go with the latter. Moreover, a critical point appears to be the difficulty in connecting local actions and global effects, the need for systemic reasonings that are capable of producing the "mechanism" with which to establish a situation of equilibrium.