Wireless sensor networks are deployed to observe remote or sensitive environments. To avoid difficult or dangerous manipulations after the deployment, power-saving strategies are used to prolong the network lifetime. Selecting active sensors, that perform the monitoring task while passive ones save energy, is one of them. The ensuing sensor area coverage issue is thus formulated as follows: every part of the deployment area, initially sensed by n deployed sensors, must be sensed by at least k active ones (k varying between 1 and n). This chapter investigates proposed techniques to designate those sensors along with existing assumptions and tools that they use.