This paper reviews various approach used in acoustic emission (AE) testing of structures so that further improvements can be realized in this important application of AE technology. In the past half century, many successful AE tests of structures have been completed, but quite often details remained private. Here, we attempt to organize the AE methodology in four steps. 1. Primary sources of brittle fracture, micro or macro cracks in contrast to secondary sources of friction or fretting, rust, etc. 2. Kaiser effects, arising from the irreversibility of AE, allow the detection of prior loading level and of damage states. 3. Source Location: This approach identifies the area of integrity loss. 4. Source Characterization: Combined AE parameters give good insight to the flaw types, but many other methods, including attenuation-corrected signal amplitude, signal frequency, waveform and wave propagation analysis and moment tensor analysis, may be useful. Avenues for better AE technology are suggested.