This article presents a review of X-ray spectroscopic diagnostic and measurement techniques as applied to laser plasma interaction and laser fusion studies. As a matter of definition we restrict our attention to the range of a several hundred eV to about 100 keV. We deal with both the basic measurement concepts and the instrumental techniques. First a brief review of the physical phenomena and parameter ranges involved is given. We then deal with specific X-ray spectroscopic instruments and methods that are useful in laser plasma X-ray spectroscopy. A discussion is given of various modeling techniques and how they can be compared with experimental measurements.