The most fundamental assessment of monitored rotating machinery vibration is, of course, provided by the ever important factors illustrated in Figure 7.1. That is, how large is the vibration and how is it trending. For those who are operating a vibration problem machine on a day-to-day basis, these two pieces of vibration information are often all that the operators use to make operational decisions. However, over the last 40 years the quite advantageous application of the FFT spectrum analysis in troubleshooting rotating machinery vibration problems has sensitized the general community of plant operators to the considerable value of vibration signal analyses in diagnosing the source of vibration problems whose solutions would otherwise be far more elusive. As illustrated in Figure 7.14, portable hand-held vibration analyzer data loggers are now pretty standard maintenance and troubleshooting tools in many types of machinery-intensive plants. There are other less commonly used signal analysis tools that are now beginning to find their way into rotating machinery vibration analysis. This chapter has the dual objectives of (a) introducing the frequently used and presently emerging machinery vibration signal analysis tools and (b) explaining the use of these tools combined with accumulated industry-wide experience in order to help identify specific sources of vibration.