We show how a slightly lossy superlens of thickness d cloaks collections of polarizable line dipoles or point dipoles or finite energy dipole sources that lie within a distance of d/2 of the lens. In the limit as the loss in the lens tends to zero, these become essentially invisible from the outside through the cancelling effects of localized resonances generated by the interaction of the source and the superlens. The lossless perfect Veselago lens has attracted a lot of debate. It is shown that as time progresses the lens becomes increasingly opaque to any physical dipole source located within a distance d/2 from the lens and which has been turned on at time t=0. Here a physical source is defined as one which supplies a bounded amount of energy per unit time. In fact the lens cloaks the source so that it is not visible from behind the lens either. For sources which are turned on exponentially slowly there is an exact correspondence between the response of the perfect lens in the long time constant limit and the response of lossy lenses in the low loss limit. This is joint work with Nicolae Nicorovici and Ross McPhedran.