Each year, nearly 4 million dogs will enter one of over 13,000 animal shelters operating in the United States. We review programmes implemented at shelters aimed at increasing the likelihood of adoption. The morphology of shelter dogs plays a large role in in-kennel adopter selection, but their behaviour is also influential in out-of-kennel adopter interactions. Previous studies suggest that dogs have the ability to readily learn new behaviours at the shelter, and programmes designed to improve behaviour of the dogs can increase adoption rates. Whilst human interaction has been well-established to improve behavioural and physiological outcomes of dogs living in shelters, analysis of the effects of sensory, environmental, and social-conspecific enrichment has not resulted in clear conclusions. We also review the literature on the relinquishment of owned dogs and return rates of previously adopted dogs. Whilst owner- and dog-related risks to relinquishment are discussed, we show that there is a notable lack of research into programmes that address issues that may prevent the initial surrender of dogs to shelters, or that could prevent re-relinquishment. It is likely that factors, unrelated to the dog, play a larger role than previously believed. Suggestions for further research include multi-site studies, investigations into the efficacy of in-shelter enrichment programmes, predictive validity of behavioural assessments, understanding of adopter behaviour at the shelter, and programmes within the community focused on keeping dogs in their homes.