Measurements of parameters of small-size plasmas are very challenging because many traditional diagnostic approaches cannot be used. Constructive coherent microwave scattering (CMS) offers a convenient diagnostic solution for such small plasmas. This work reviews the development and applications of constructive coherent microwave scattering by the Electric Propulsion and Plasma Laboratory at Purdue University. It presents fundamentals of CMS with an emphasis on Thomson, collisional, and Rayleigh scattering in short, thin, unmagnetized plasma media. Additionally, we review examples of CMS application for diagnostics of temporally resolved plasma dynamics and electron decay, photoionization rates, electron momentum-transfer collision frequencies, and number densities of selective species in gaseous mixtures. These applications are relevant for various research fields including strong field and femtosecond filamentation physics, plasma-assisted ignition and combustion, and combustion and spacecraft electric propulsion diagnostics.