In the last few decades cooperation among fluid dynamicists and geomorphologists has allowed the construction of a rational framework for the quantitative understanding of several geomorphologic processes involved in the shaping of the Earth's surface. Particular emphasis has been given to the dynamics of sedimentary patterns, features arising from the continuous dynamic interaction between the motion of a sediment-carrying fluid and an erodible boundary. It is this interaction which ultimately gives rise to the variety of natural forms, often displaying a high degree of regularity, observed in rivers, estuaries, coasts, as well as in the deep submarine environment. Theoretical analyses and laboratory experiments have shown that the nature of most of the observed patterns is related to fundamental instability mechanisms whose particular character lies in the fact that it is the mobile interface between the fluid and the erodible boundary, rather than the flow itself, that is unstable. Developments have been general enough to reach the status of a distinct branch of fluid mechanics, geomorphological fluid mechanics. This paper concentrates on the mechanics of fluvial meandering. Our aim is to provide the reader with a systematic overview of the fundamental aspects of the subject, assessing, with the help of recent and novel results, settled as well as unsettled issues.