Wireless sensor networks (WSNs) have recently attracted a great deal of attention due to their numerous attractive applications in many different fields. Sensors and WSNs possess a number of special characteristics that make them very promising in a wide range of applications, but they also put on them lots of constraints that make issues in sensor network particularly challenging. These issues may include topology control, routing, coverage, security, data management and many others. Among them, coverage problem is one of the most fundamental ones for which a WSN has to watch over the environment such as a forest (area coverage) or set of subjects such as collection of precious renaissance paintings (target of point coverage) in order for the network to be able to collect environment parameters, and maybe further monitor the environment. In this dissertation, we highly focus on the area coverage problem. With no assumption of sensors’ locations (i.e., the sensor network is randomly deployed), we only consider distributed and parallel scheduling methods with the ultimate objective of maximizing network lifetime. Additionally, the proposed solutions (including algorithms, a scheme, and a framework) have to be energy-efficient. Generally, we investigate numerous generalizations and variants of the basic coverage problem. Those problems of interest include k-coverage, composite event detection, partial coverage, and coverage for adjustable sensing range network. Various proposed algorithms. In addition, a scheme and a framework are also suggested to solve those problems. The scheme, which is designed for emergency alarming applications, specifies the guidelines for data and communication patterns that significantly reduce the energy consumption and guarantee very low notification delay. For partial coverage problem, we propose a universal framework (consisting of four strategies) which can take almost any complete-coverage algorithm as an input to generate an algorithm for partial coverage. Among the four strategies, two pairs of strategies are trade-off in terms of network lifetime and coverage uniformity. Extensive simulations are conducted to validate the efficiency of each of our proposed solutions.