Hierarchical structure formation in a LCDM cosmology gives rise to virialized dark matter halos that contain a wealth of subtructure. Being able to accurately predict the abundance and demographics of dark matter subhaloes is of paramount importance for many fields of astrophysics: gravitational lensing, galaxy evolution, and even constraining the nature of dark matter. Dark matter substructure is subject to tidal stripping and tidal heating, which are highly non-linear processes and therefore best studied using numerical N-body simulations. Unfortunately, as I will demonstrate, state-of-the-art cosmological simulations are unable to adequately resolve the dynamical evolution of dark matter substructure. They suffer from a dramatic amount of artificial subhalo disruption as a consequence of both inadequate force softening and discreteness noise amplification in the presence of a tidal field. I discuss implications for a variety of astrophysical applications, and briefly discuss potential ways forward.