Large-scale, self-organizing wireless sensor and mesh network deployments are being driven by recent technological developments such as The Internet of Things (IoT), Smart Grids and Smart Environment applications. Efficient use of the limited energy resources of wireless sensor network (WSN) nodes is critically important to support these advances, and application of topology control methods will have a profound impact on energy efficiency and hence battery lifetime. In this survey, we focus on the energy efficiency issue and present a comprehensive study of topology control techniques for extending the lifetime of battery powered WSNs. First, we review the significant topology control algorithms to provide insights into how energy efficiency is achieved by design. Further, these algorithms are classified according to the energy conservation approach they adopt, and evaluated by the trade-offs they offer to aid designers in selecting a technique that best suits their applications. Since the concept of «network lifetime» is widely used for assessing the algorithms' performance, we highlight various definitions of the term and discuss their merits and drawbacks. Recently, there has been growing interest in algorithms for non-planar topologies such as deployments in underwater environments or multi-level buildings. For this reason, we also include a detailed discussion of topology control algorithms that work efficiently in three dimensions. Based on the outcomes of our review, we identify a number of open research issues for achieving energy efficiency through topology control. © 1998-2012 IEEE.