Suicidal behavior in older adults (65 years old and over) is a major public health issue in many countries. Suicide rates increase during the life course and are as high as 48.7/100,000 among older white men in the USA. Specific health conditions and stress factors increase the complexity of the explanatory model for suicide in older adults. A PubMed literature search was performed to identify most recent and representative studies on suicide risk factors in older adults. The aim of our narrative review was to provide a critical evaluation of recent findings concerning specific risk factors for suicidal thoughts and behaviors among older people: psychiatric and neurocognitive disorders, social exclusion, bereavement, cognitive impairment, decision making and cognitive inhibition, physical illnesses, and physical and psychological pain. We also aimed to approach the problem of euthanasia or physician-assisted suicide in older adults. Our main findings emphasize the need to integrate specific stress factors, such as feelings of social disconnectedness, neurocognitive impairment or decision making, as well as chronic physical illnesses and disability in suicide models and in suicide prevention programs in older adults. Furthermore, the chronic care model should be adapted for the treatment of older people with long-term conditions in order to improve the treatment of depressive disorders and the prevention of suicidal thoughts and acts.