This article provides a brief overview of both established and novel ellipsometry techniques, as well as their applications. Ellipsometry is an indirect optical technique, in that information about the physical properties of a sample is obtained through modeling analysis. Standard ellipsometry is typically used to characterize optically isotropic bulk and/or layered materials. More advanced techniques such as Mueller ellipsometry, also known as polarimetry in the literature, are necessary for the complete and accurate characterization of anisotropic and/or depolarizing samples that occur in many instances, both in research and in real-life activities. In this article, we cover three main subject areas: Basic theory of polarization, standard ellipsometry, and Mueller ellipsometry. The first section is devoted to a short, pedagogical introduction of the formalisms used to describe light polarization. The second section is devoted to standard ellipsometry. The focus is on the experimental aspects, including both pros and cons of commercially available instruments. The third section is devoted to recent advances in Mueller ellipsometry. Application examples are provided in the second and third sections to illustrate how each technique works.

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