Power is one of the most critical resources in wireless ad hoc networks when the wireless nodes are powered by batteries only. In this chapter, we study how to assign each wireless node a transmission power (level) such that the resulting communication graph has certain desired properties. Recently, much progress has been made on algorithmic and probabilistic studies of various power-assignment problems. These problems come in many flavors, depending on the power-requirement function and the connectivity constraint, and minimizing the total power consumption by all wireless nodes in a network is NP-hard for most versions. We study some of the best-known approximation algorithms for minimizing the total power consumption in the network and sketch useful heuristics with practical value. Observe that a majority of the power-assignment problems use the same network setting as some problems we studied in other chapters, especially about topology control; some questions are different (although they look similar). For example, in this chapter, we study the power-assignment problem by minimizing the total power while the resulting network is connected. A similar problem is to find a broadcast tree that has the minimum total power consumption. The difference here is that the leaf nodes are not required to transmit for broadcast applications, whereas all nodes are required to transmit for a tree spanning all nodes to result in a connected network.