Some of the largest and most persistent circulation errors in global numerical weather prediction and climate models are attributable to the inadequate representation of the impacts of orography on the atmospheric flow. Existing parametrization approaches attempting to account for unresolved orographic processes, such as turbulent form drag, low-level flow blocking or mountain waves, have been successful to some extent. They capture the basic impacts of the unresolved orography on atmospheric circulation in a qualitatively correct way and have led to significant progress in both numerical weather prediction and climate modelling. These approaches, however, have apparent limitations and inadequacies due to poor observational evidence, insufficient fundamental knowledge and an ambiguous separation between resolved and unresolved orographic scales and between different orographic processes. Numerical weather prediction and climate modelling has advanced to a stage where these inadequacies have become critical and hamper progress by limiting predictive skill on a wide range of spatial and temporal scales. More physically based approaches are needed to quantify the relative importance of apparently disparate orographic processes and to account for their combined effects in a rational and accurate way in numerical models. We argue that, thanks to recent advances, significant progress can be made by combining theoretical approaches with observations, inverse modelling techniques and high-resolution and idealized numerical simulations.