Abstract: This paper examines current understanding of the influence of orographic flow dynamics on the turbulent transport of momentum and scalar quantities above complex terrain. It highlights three key low-level orographic flow phenomena governed by gravity-wave dynamics: Foehn flow, atmospheric rotors and gravity-wave modulation of the stable boundary layer. Recent observations and numerical simulations are used to illustrate how these flows can cause significant departures from the turbulent fluxes, which occur over flat terrain. Orographically forced fluxes of heat, moisture and chemical constituents are currently unaccounted for in numerical models. Moreover, whilst turbulent orographic drag parameterisation schemes are available (in some models), these do not represent the large gravity-wave scales associated with foehn dynamics; nor do they account for the spatio-temporal heterogeneity and non-local turbulence advection observed in wave-rotor dynamics or the gravity waves, which modulate turbulence in the boundary layer. The implications for numerical models, which do not resolve these flows, and for the parametrisation schemes, which should account for the unresolved fluxes, are discussed. An overarching need is identified for improved understanding of the heterogeneity in sub-grid-scale processes, such as turbulent fluxes, associated with orographic flows, and to develop new physically-based approaches for parameterizing these processes.