Trophy hunting can be a major component of conservation strategies for large mammals, but it must be both ecologically and evolutionarily sustainable. Selection will not necessarily lead to evolution. To affect evolution, selective hunting must target an inheritable trait and be stronger than natural or sexual selective pressures that it may oppose. For some ungulates, horn or antler size, the trait usually targeted by trophy hunting, is strongly correlated with mating success, often in interaction with male age. For other species the correlation is weak, and for most species it is unknown. Selective hunting is more likely to induce genetic change if it targets a trait expressed early in life, if it causes strong trait-based selective mortality, and if hunting regulations remain similar over a wide area and for multiple generations. Protected areas may be a source of unselected males that could dampen artificial selection, but only if those males migrate out of protected areas for the rut after the hunting season, otherwise they are likely to be shot before they breed. Using long-term data from bighorn sheep, Stone's sheep, red deer, mountain goat and chamois I will illustrate when selective hunting is most likely to select and what management strategies can be used to prevent or reduce this selective effect. Those strategies include a reduction in hunting pressure, an increase in harvest age, and protection of males that emigrate from protected areas to breed.