Seismic site characterization attempts to quantify seismic wave behavior at a specific location based on near-surface geophysical properties, for the purpose of mitigating damage caused by earthquakes. In recent years, techniques for estimating near-surface properties for site characterization using geophysical observations recorded at the surface have become an increasingly popular alternative to invasive methods. These observations include surface-wave phenomenology such as dispersion (velocity-frequency relationship) as well as, more recently, full seismic waveforms. Models of near-surface geophysical properties are estimated from these data via inversion, such that they reproduce the observed seismic observations. A wide range of inverse problems have been considered in site characterization, applying a variety of mathematical techniques for estimating the inverse solution. These problems vary with respect to seismic data type, algorithmic complexity, computational expense, physical dimension, and the ability to quantitatively estimate the uncertainty in the inverse solution. This paper presents a review of the common inversion strategies applied in seismic site characterization studies, with a focus on associated advantages/disadvantages as well as recent advancements.