Trap-Neuter-Return (TNR) programs, in which stray cats are captured, neutered and returned to the environment are advocated as a humane, ethical alternative to euthanasia. We review the TNR literature in light of current debate over whether or not there should be further TNR trials in Australia. We revisit the problems arising from stray cats living in association with human habitation and estimate how many stray cats would have to be processed through a scientifically-guided TNR program to avoid high euthanasia rates. We also identify 10 ethical and welfare challenges that have to be addressed: we consider the quality of life for stray cats, where they would live, whether the TNR process itself is stressful, whether TNR cats are vulnerable to injury, parasites and disease, can be medically treated, stray cats’ body condition and diet, and their impacts on people, pet cats, and urban wildlife, especially endemic fauna. We conclude that TNR is unsuitable for Australia in almost all situations because it is unlikely to resolve problems caused by stray cats or meet ethical and welfare challenges. Targeted adoption, early-age desexing, community education initiatives and responsible pet ownership have greater promise to minimize euthanasia, reduce numbers rapidly, and address the identified issues.