In this talk we aim to describe well-balanced Lagrange-projection schemes that can be exploited for the numerical simulation of not only geophysical but also biological flows. In a few words, such methods are composed of two steps: first, the mathematical model is expressed in Lagrangian coordinates. Then, once the Lagrangian solution has been found, it is projected back into Eulerian coordinates. This strategy can also easily be interpreted as a splitting: the Lagrangian step takes into account the acoustic effects of the flow, while the projection step is dedicated to the transport phenomena. This kind of acoustic-transport splitting is of particular interest in many geophysical flows as it provides a natural time scale decomposition leading to very efficient implicit-explicit (IMEX) schemes. In particular, we focus on applications to sediment transport and stratified flows. Depending on the mathematical model, we either extend the well-balanced numerical method to second-order of accuracy or develop their IMEX version.