FEM and BEM simulations with the gypsilab framework. Gypsilab is a Matlab framework which aims at simplifying the development of numerical methods that apply to the solution of problems in multiphysics, in particular, those involving FEM or BEM simulations. The peculiarities of the framework, with a focus on its ease of use, are shown together with the methodology that have been followed for its development. Example codes that are short though representative enough are given both for FEM and BEM applications. A performance comparison with FreeFem++ is provided, and a particular emphasis is made on problems in acoustics and electromagnetics solved using the BEM and for which compressed $mathcal{H}$-matrices are used.