— In this paper, we study coverage with connectivity properties in large wireless sensor networks. We consider three classes: full coverage with connectivity, partial coverage with connectivity, and constrained coverage with connectivity. We outline two simple network topologies to satisfy the constrained coverage with connectivity criterion. We compare the surveillance performance and deployment cost for networks with different coverage with connectivity criteria. Together, they cover a whole spectrum of surveillance quality in wireless sensor networks at different cost. We outline potential research topics in the area.