The ultimate resource in wireless networks is transmission power. The system stability and the resource sharing algorithms all rely on well functioning power control. To realistically address resource management algorithms, it is important to consider fundamental limitations of the radio resource and of power control. Exact and approximate capacity expressions are derived and related to Quality of Service (QoS) requirements of services. Power control is subject to limited update rate, limited feedback bandwidth, time delays, measurement errors, feedback errors and filtering effects which all affect the resulting performance. Simulations further illustrate the hampering effects and motivates models of power control inaccuracies. Copyright © 2004 John Wiley & Sons, Ltd.