In this thesis, we present a distributed model predictive control (MPC) framework for the cooperative control of multi-agent systems. The agents are dynamically decoupled but connected through a communication network and are required to perform general cooperative tasks that may go beyond classical setpoint stabilization. The cooperative task is encoded as a shared objective function that is minimized collectively by the agents. Each agent optimizes an artificial reference as an intermediate step towards the cooperative objective, along with a control input to track it. This introduces a flexible mechanism to guide the agents' interaction towards a solution to the cooperative task. Importantly, this solution is not predetermined but emerges from the optimized interactions of the agents. Various further advantages of the framework are discussed. The framework readily handles, but is not limited to, common and important cooperative tasks such as consensus and synchronization, in which agents must agree on an a priori unknown output value or trajectory. The first contribution of this thesis is the derivation of a global closed-loop transient performance bound for MPC for tracking. The second contribution of this thesis is a sequential distributed MPC method for cooperative tasks defined at equilibria. The third contribution of this thesis is an iterative distributed MPC method for cooperative tasks defined on periodic trajectories.