The concept of entanglement renormalisation will be introduced in a pedagogical manner. Next, as an application, we will use it to study boundary critical phenomonena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum critical ground states. Here we show that, by adding a boundary to the scale invariant MERA, an accurate approximation to the critical ground state of an infinite chain with a boundary is obtained, from which one can extract boundary scaling operators and their scaling dimensions. We test the approach by studying the quantum critical Ising model with free and fixed boundary conditions.