The equations of fluid mechanics can be used to describe natural processes over a wide range of scales, from the behaviour of micro-organisms to astrophysics. Each of these processes is in turn often controlled by internal interactions on widely different scales. Numerical methods able to efficiently resolve these interactions are in combination with theoretical analysis and lab experiments an essential tool for advancing our understanding. I will give a general overview of the hierarchical numerical methods I have worked on, as implemented within the free software Gerris Flow Solver (http://gfs.sf.net) and Basilisk (http://basilisk.fr) and discuss a range of applications including microscale high-energy droplet dynamics, multiphase and complex flows and tsunamis.