Understanding mixing through the stably stratified regions of stars is critical in placing them correctly on evolutionary tracks and interpreting abnormal abundances observed at their sufaces. Asteroseismic studies depend on 1D evolution models, so correctly determining mixing rates to improve these is essential. Here, I will present our study of vertical mixing driven by internal gravity waves (IGWs) based on multi-dimensional hydrodynamical simulations with our fully compressible code MUSIC (Baraffe et al. 2023; Le Saux et al. 2023; Morton et al., in prep.). Among others, two mechanisms of mixing by IGWs in stars are commonly quoted: firstly, thermal diffusion providing a non-restorative effect to the waves, leaving material 'swept away' from its equilibrium (Press 1981; Zahn et al. 1997), and secondly waves sustaining a strong enough shear to create weak localised turbulence (García López & Spruit 1991). We show that for massive main-sequence stars, neither of these mechanisms are likely to be significant enough to produce the mixing required to obtain correct evolutionary tracks, and even less so for stars evolved past zero-age main sequence. Furthermore, we warn that tracer particle methods used to measure mixing by IGWs are prone to subtle numerical artefacts due to integration of periodic flows over long time scales. Diffusion coefficients based on such methods are used in stellar evolution codes to interpret observations and should be taken with caution.