Wild mammal transport is an important component of conservation translocation as well as the economic wildlife trade. This article reviews the physiological responses to transport that have been measured in wild mammalian species, factors associated with these responses, and interventions that have been applied to mitigate these responses. By organizing the literature review along the “five domains model” of animal welfare, namely, the physical-functional domains (nutrition, environment, health, behavior) and the mental domain (mental state), it can be demonstrated that wild mammal transport is associated with challenges to ensuring positive animal welfare in all five domains. Transported wild mammals can experience dehydration, catabolism, fatigue, immunosuppression, behavioral changes, and stress. Factors influencing these physiological responses to transport have only been researched in a few studies encompassing species, journey length, ambient temperature, vehicle motion, stocking density, orientation, habituation, vehicle speed allowance, and road type. The administration of tranquilizers has been shown to mitigate negative physiological responses to transport. There is a need to further investigate species and situation-specific physiological responses to transport and factors associated with these responses in order to identify challenges to ensuring animal welfare and improving translocation success.