Orographic gravity waves (also known as mountain waves) exert a drag force on the mountains that generate them, and this creates a reaction force applied back on the atmosphere. These waves occur in stratified airflow over orography, and must be parametrized in global weather prediction models, because their associated drag typically acts at horizontal scales of ~10km, unresolved by those models. Although for realistic atmospheric profiles these waves are exceedingly complex, in the limit of low-amplitude waves it is possible to explicitly calculate the drag using linear theory for some limit cases, which are useful in guiding the development of drag parametrizations. One of these limits is that of slowly-varying atmospheric wind and static stability profiles, for which the WKB approximation may be used to solve the wave equation in Fourier space, and derive the impact of, for example, vertical wind shear on the drag. Although the full wave field may not be obtained in a compact form, the effect of critical levels on the wave momentum flux may be evaluated using complex integration techniques. Another useful limit is that of piecewise-constant atmospheric profiles, for which wave trapping at low levels may occur. In this case, although the wave field may only be determined analytically far from its source (as shown by Scorer), the associated drag may be evaluated exactly using again complex integration. In this talk, these aspects will be discussed in the context of contributions given in recent years to the study of mountain wave drag.