Power quality monitoring has expanded from a means to investigate customer complaints to an integral part of power system performance assessments. Besides special purpose power quality monitors, power quality data are collected from many other monitoring devices on the system (intelligent relays, revenue meters, digital fault recorders, etc.). The result is a tremendous volume of measurement data that is being collected continuously and must be analyzed to determine if there are important conclusions that can be drawn from the data. It is a significant challenge due to the wide range of characteristics involved, ranging from very slow variations in the steady state voltage to microsecond transients and high frequency distortion. This paper describes some of the problems that can be evaluated with both offline and online analyses of power quality measurement data. These applications can dramatically increase the value of power quality monitoring systems and provide the basis for ongoing research into new analysis and characterization methods and signal processing techniques.