Public opposition to non-human primate (NHP) experiments is significant, yet those who defend them cite minimal harm to NHPs and substantial human benefit. Here we review these claims of benefit, specifically in neuroscience, and show that: a) there is a default assumption of their human relevance and benefit, rather than robust evidence; b) their human relevance and essential contribution and necessity are wholly overstated; c) the contribution and capacity of non-animal investigative methods are greatly understated; and d) confounding issues, such as species differences and the effects of stress and anaesthesia, are usually overlooked. This is the case in NHP research generally, but here we specifically focus on the development and interpretation of functional magnetic resonance imaging (fMRI), deep brain stimulation (DBS), the understanding of neural oscillations and memory, and investigation of the neural control of movement and of vision/binocular rivalry. The increasing power of human-specific methods, including advances in fMRI and invasive techniques such as electrocorticography and single-unit recordings, is discussed. These methods serve to render NHP approaches redundant. We conclude that the defence of NHP use is groundless, and that neuroscience would be more relevant and successful for humans, if it were conducted with a direct human focus. We have confidence in opposing NHP neuroscience, both on scientific as well as on ethical grounds.