The proportion of people with dementia has been increasing yearly, and the decision-making capacity of these people has become a major concern in fields such as the financial industry and in medical settings. In this narrative review, we discuss decision-making in people with Alzheimer’s disease (AD), and we propose the support for decision-making in people with AD, especially financial and medical decision-making. We summarize several hypotheses and theories on the decision-making capacity of people with AD. These include the frontal lobe hypothesis, physiological theory, dysfunction of the hypothalamic-pituitary-adrenal (HPA) axis, and the Person-Task-Fit (PTF) framework. Both internal and external factors can affect decision-making by people with AD. Internal factors are affected by changes in the brain and neurotransmitters, as well as alterations in cognitive ability and emotion. External factors include task characters, task contents, and situation influence. Since feedback has a significant effect on decision-making capacity, a series of suggestions may be helpful to improve this capacity, such as explicit advice, simple options, pleasant rewards, the Talking Mats approach, memory and organizational aid, support by caregivers, cognitive training and feedback. Thus, in providing decision-making support for people with AD, it is important to identify the internal and external factors that impair this process and to deal with these factors.