The flow equations of the renormalization group allow to analyse the perturbative \(n\)-point functions of renormalizable quantum field theories. Rigorous bounds obtained from the flow equations  permit to control large momentum behaviour, infrared singularities and large order behaviour in the number of loops and arguments \(n\). We explain how this method gives a rigorous proof of the renormalizability of the massive \(\phi_4^4\) theory on \({\mathbb{R}}^4\)  without analyzing Feynmann diagrams. The proof is based on proving bounds which are uniform in the cutoff and thus directly lead to renormalizability. We will also briefly discuss how the method of the flow equations can be used to investigate the renormalizability of the massive \(\phi_4^4\) scalar field theory on the semi-infinite space, which is the simplest model to study surface effects in quantum field theory.