This paper addresses the topology control problem for large wireless networks that are modelled by an infinite point process on a two-dimensional plane. Topology control is the process of determining the edges in the network by adjusting the transmission radii of the nodes. Topology control algorithms should be based on local decisions, be adaptive to changes, guarantee full connectivity and support efficient routing. We present a family of topology control algorithms that, respectively, achieve some or all of these requirements efficiently. The key idea in our algorithms is a concept that we call monotone percolation. In classical percolation theory, we are interested in the emergence of an infinitely large connected component. In contrast, in monotone percolation we are interested in the existence of a relatively short path that makes monotonic progress between any pair of source and destination nodes. Our key contribution is that we demonstrate how local decisions on the transmission radii can lead to monotone percolation and in turn to efficient topology control algorithms.