Clusters represent a new class of laser pulse targets which show both the properties of underdense and of overdense plasmas. We present analytical and numerical results (based on 2D- and 3D-PIC simulations) of the Coulomb explosion of the ion cloud that is formed when a cluster is irradiated by a high-intensity laser pulse. For laser pulse intensities in the range of 1021−1022 W/cm2, the laser light can rip electrons from atoms almost instantaneously and can create a cloud made of an electrically nonneutral plasma. Ions can then be accelerated up to high energy during the Coulomb explosion of the cloud.