Dementia is a serious threat to social sustainability. As life expectancy increases, more people are developing dementia. At the same time, demographic change is reducing the economically active part of the population. Care of people with dementia imposes great emotional and financial strain on sufferers, their families and society at large. In response, significant research resources are being focused on dementia. One research thread is focused on using computer technology for monitoring people in at-risk groups to improve rates of early diagnosis. In this paper we provide an overview of dementia monitoring research and identify a set of scientific challenges for the engineering of dementia-monitoring software, with implications for other mental health self-management systems.