Alzheimer’s disease (AD) is a chronic neurodegenerative disorder characterised by cognitive impairment and numerous pathologies, including β-amyloid (Aβ) and Tau proteopathies, altered immune responses, and brain atrophy. Despite hundreds of years of investigations into its underlying pathogenesis, the aetiology of AD is not clearly understood. AD diagnostic criteria are not effective at identifying pre-clinical patients and current AD treatments cannot postpone or reverse disease progression. The development of non-human primate (NHP) models of AD is urgently required due to their close phylogenetic relationship to humans, similar neuroanatomy, comparable genetics, and high complexity of high-order cognitive functions, making them a better model of AD than rodents. We compared and contrasted AD-associated pathological features and behavioural alterations manifested between naturally aged spontaneous and induced NHP models of AD. Induced models of AD can be established using injections of Aβ oligomers, brain homogenates, neurotoxins, or formaldehyde. In recent decades, both spontaneous and induced NHP models of AD have been used to facilitate the development of neuroimaging tracers and therapeutic treatments, aiding in the translational application of lab discoveries into clinical trials involving human subjects. The establishment of a standardised NHP model of AD is expected by making a guideline concerning NHP species, types and doses of inducers, frequency of injections, and duration of inoculation. Its development can be facilitated by a comprehensive assessment of NHPs, including all AD-associated pathologies and a wide range of behavioural examinations. NHP models of AD have contributed to AD research and their evolution is expected to better recapitulate AD features and present greater translational potential in the near future.