abstract: The volume preserving mean curvature flow is the gradient flow of the area functional under the fixed enclosed volume constraint. We point out differences of this non-local flow to the classical mean curvature flow, for example non-preservation of certain properties, like mean convexity and embeddedness. Then we report on progress in studying the fundamental behavior and the formation of finite time singularities of the flow in the closed setting. This talk is based on work with Ben Lambert (Leeds).