Magnetohydrodynamic waves permeate the solar atmosphere but despite being regularly observed and analysed in great detail, their role in the energy transport through the solar atmosphere and in heating the solar corona remains unclear. This is largely due to the complexity and dynamism of the solar atmosphere where the combination of gravitational stratification, magnetic field expansion and local density inhomogeneities leads to complicated coupling and interactions between different layers of the solar atmosphere. Various modelling techniques, including numerical simulations and forward modelling, allow us to tackle this complexity and investigate the various wave processes. Constraints on the energy budget, identification of the dissipation mechanisms and determination of the spatial and temporal scales of the energy deposition and the observational signatures can thus be obtained. In this RAS Specialist Discussion meeting, we aim to bring together experts in numerical modelling, observational detection and theoretical analysis of wave-based heating mechanism to shed light on the role of MHD waves in coronal heating. We will focus in particular on recent advancements in this field due to the use of increasingly complex numerical experiments.