Methods and apparatus for processing discovery signals and/or generating alerts based on received discovery signals are described. In at least some embodiments, alert signal generation is performed on a selective basis in response to received discovery signals. In at least some embodiments a user is given at least some control over alert generation with the user being able to indicate types of signals which should not trigger generation of an alert, the minimum permitted frequency of particular alerts or types of alerts and/or time or location constraints which are considered when a device determines whether or not to generate an alert in response to a received discovery signal. While user control of discovery signal processing and alert generation are provided, automatic control or adjustment of discovery signal processing and alert generation may also be implemented or the automatic control may be implemented as an alternative to the user control.