From 19th to 22nd November 2018, 26 researchers representing nine countries and a variety of academic disciplines met in Snekkersten, Denmark, to reach evidence-based consensus about physical activity and older adults. It was recognised that the term 'older adults' represents a highly heterogeneous population. It encompasses those that remain highly active and healthy throughout the life-course with a high intrinsic capacity to the very old and frail with low intrinsic capacity. The consensus is drawn from a wide range of research methodologies within epidemiology, medicine, physiology, neuroscience, psychology and sociology, recognising the strength and limitations of each of the methods. Much of the evidence presented in the statements is based on longitudinal associations from observational and randomised controlled intervention studies, as well as quantitative and qualitative social studies in relatively healthy community-dwelling older adults. Nevertheless, we also considered research with frail older adults and those with age-associated neurodegenerative diseases, such as Alzheimer's and Parkinson's disease, and in a few cases molecular and cellular outcome measures from animal studies. The consensus statements distinguish between physical activity and exercise. Physical activity is used as an umbrella term that includes both structured and unstructured forms of leisure, transport, domestic and work-related activities. Physical activity entails body movement that increases energy expenditure relative to rest, and is often characterised in terms of intensity from light, to moderate to vigorous. Exercise is defined as a subset of structured physical activities that are more specifically designed to improve cardiorespiratory fitness, cognitive function, flexibility balance, strength and/or power. This statement presents the consensus on the effects of physical activity on older adults' fitness, health, cognitive functioning, functional capacity, engagement, motivation, psychological well-being and social inclusion. It also covers the consensus on physical activity implementation strategies. While it is recognised that adverse events can occur during exercise, the risk can be minimised by carefully choosing the type of activity undertaken and by consultation with the individual's physician when warranted, for example, when the individual is frail, has a number of co-morbidities, or has exercise-related symptoms, such as chest pain, heart arrhythmia or dizziness. The consensus was obtained through an iterative process that began with the presentation of the state-of-the-science in each domain, followed by group and plenary discussions. Ultimately, the participants reached agreement on the 30-item consensus statements.