In modern wireless networks, devices are able to set the power for each transmission carried out. Experimental but also theoretical results indicate that such power control can improve the network capacity significantly. We study this problem in the physical interference model using SINR constraints. In the SINR capacity maximization problem, we are given n pairs of senders and receivers, located in a metric space (usually a so-called fading metric). The algorithm shall select a subset of these pairs and choose a power level for each of them with the objective of maximizing the number of simultaneous communications. This is, the selected pairs have to satisfy the SINR constraints with respect to the chosen powers. We present the first algorithm achieving a constant-factor approximation in fading metrics. The best previous results depend on further network parameters such as the ratio of the maximum and the minimum distance between a sender and its receiver. Expressed only in terms of n, they are (trivial) Omega(n) approximations. Our algorithm still achieves an O(log n) approximation if we only assume to have a general metric space rather than a fading metric. Furthermore, by using standard techniques the algorithm can also be used in single-hop and multi-hop scheduling scenarios. Here, we also get polylog(n) approximations.