The purpose of this review is to present the best available scientific knowledge on key animal welfare issues during swine transport, such as transport duration and distance, time off feed and water, rest intervals, environmental conditions, loading density, and transport of young animals, based on their impact on stress, injury, fatigue, dehydration, body temperature, mortality, and carcass and meat quality. The review was limited to this set of priority welfare issues which were identified by the National Farm Animal Care Council (NFACC) Scientific Committee to help with the development of the livestock transportation Codes of Practice. This review focuses primarily on research related to the transport of market pigs (100–135 kg) which is a reflection of the current literature available on pig transportation. This information presented here can be used to support other animal welfare codes, guidelines, standards or legislations regulating the welfare of pigs during transport. Based on the available literature, clear conclusions can be drawn on the impact of vehicle design, pre-transport fasting, control of environmental conditions and loading density on the welfare of pigs during transport and on pork quality. However, the effects of journey duration are still unclear and a recommendation on the maximum transport time cannot be provided. Further studies investigating the impact of factors, such as ambient conditions within the transport vehicle, loading density at extreme ambient conditions, travel distances, maximum travel duration, rest/stop duration, and management of pigs during rest stops are required. More specifically, further research in relation to the welfare of market weight, newly weaned and breeding pigs, and cull sows and boars during transport is needed.