The rapid progress in wireless communication and embedded micro-sensing MEMS technologies has made wireless sensor networks possible. Such environments may have many inexpensive wireless nodes, each capable of collecting, storing, and processing environmental information, and communicating with neighboring nodes. In the past, sensors were connected by wire lines. Today, this environment is combined with the novel ad hoc networking technology to facilitate inter-sensor communication. The flexibility of installing and configuring a sensor network is thus greatly improved. Recently, a lot of research activities have been dedicated to sensor networks, including physical and medium access layers and routing and transport layers. Because sensors can be spread in an arbitrary manner, one of the fundamental issues in a wireless sensor network is the coverage problem. Given a sensor network, the coverage problem is to determine how well the sensing field is monitored or tracked by sensors. In the literature, this problem has been formulated in various ways. A lot of works have been dedicated to coverage-related problems in wireless sensor networks in the past few years. These include the surveillance and exposure of sensor networks, and the concerns of coverage versus connectivity issues when deploying a sensor network. Through this chapter, we intend to provide a comprehensive survey of the literature. We also discuss some application scenarios of the coverage problem. For example, to reduce sensors’ on-duty time, those sensors that share the common sensing region and task can be turned off to conserve energy and thus extend the network lifetime.