The automation of ab initio simulations is essential in view of performing high-throughput (HT) computational screenings oriented to the discovery of novel materials with desired physical properties. In this work, we propose algorithms and implementations that are relevant to extend this approach beyond density functional theory (DFT), in order to automate many-body perturbation theory (MBPT) calculations. Notably, a novel algorithm pursuing the goal of an efficient and robust convergence procedure for GW and BSE simulations is provided, together with its implementation in a fully automated framework. This is accompanied by an automatic GW band interpolation scheme based on maximally-localized Wannier functions, aiming at a reduction of the computational burden of quasiparticle band structures while preserving high accuracy. The proposed developments are validated on a set of representative semiconductor and metallic systems.