This paper reviews the most common methods of generation of plasmas using microwaves with special emphasis on recently developed microwave plasma (MWP) sources for analytical applications. The art and science of microwave plasma optical and mass spectroscopy instrumentation (MWP-OES/MS), and the applications are briefly presented, including very recent advances in the field as of 2012. The design and operation of MWPs is discussed to provide a basic understanding of the most important selection criteria when designing MWP systems. The various plasma generation systems described include single-electrode capacitive microwave plasmas, electrodeless inductively coupled plasmas, multi-electrode systems energized with stationary or rotating fields. We also discuss various technical realizations of MWP sources for selected applications. Examples of technical realizations of plasmas in closed structures (cavities), in open structures (surfatrons, planar plasma sources), and in magnetic fields (Hammer cavity) are discussed in detail. Finally, we mention micro- and mini-discharges as convenient sources for miniaturized spectrometric systems. Specific topics include fundamental aspects of MWP, i.e., recent advances in the construction of analytical MWPs (coaxially coupled cavities, strip-line technology, multi-point energizing, power combining, rotating field-excited plasmas), operational characteristics, analytical characteristics and applications. Special reference is made to coupling with OES for determination of chromatographic effluents and particle sizing. The developments in elemental and molecular MS applications in both low-power and high-power MWPs are also discussed.