Future cognitive radios will require use of both established emitter databases and local spectrum sensing to optimize their performance. The authors view these techniques as ways of estimating an RF Environment Map (RFEM), which characterizes the position, directivity, power, and modulation type of all relevant RF emitters in a geographical region of interest. Cognitive radios will make their best decisions when they have the best RFEM information available. Good RFEM estimates are facilitated by spectrum-sensing algorithms that exploit the complex statistics of modern communication signals rather than relying on simplistic energy detection. They illustrate some of the ways that such statistics can be exploited using collected modern communications signals.