Tau, a neuronal protein known to bind to microtubules and thereby regulate microtubule dynamic instability, has been shown recently to not only undergo conformational transitions on the microtubule surface as a function of increasing microtubule coverage density (i.e., with increasing molar ratio of Tau to tubulin dimers) but also to mediate higher-order microtubule architectures, mimicking fascicles of microtubules found in the axon initial segment. These discoveries would not have been possible without fine structure characterization of microtubules, with and without applied osmotic pressure through the use of depletants. Herein, we discuss the two primary techniques used to elucidate the structure, phase behavior, and interactions in microtubule/Tau mixtures: transmission electron microscopy and synchrotron small-angle X-ray scattering. While the former is able to provide striking qualitative images of bundle morphologies and vacancies, the latter provides angstrom-level resolution of bundle structures and allows measurements in the presence of in situ probes, such as osmotic depletants. The presented structural characterization methods have been applied both to equilibrium mixtures, where paclitaxel is used to stabilize microtubules, and also to dissipative nonequilibrium mixtures at 37 degrees C in the presence of GTP and lacking paclitaxel. Institutes of Health under award numbers R01-NS13560 and R01-NS35010 (tubulin purification and protein Tau isoform purification from plasmid preparations). U. R. acknowledges support from the Israel Science Foundation (Grant 656/17). M.C.C. was supported by NRF2014R1A1A2A16055715, 2014M2B2A4030706, and APCTP. The x-ray diffraction work was carried out at the Stanford Synchrotron Radiation Lightsource, a Directorate of SLAC National Accelerator Laboratory and an Office of Science User Facility operated for the US DOE Office of Science by Stanford University. The SSRL Structural Molecular Biology Program which supports BL4-2 is funded by the DOE Biological and Environmental Research and the NIH National Institute of General Medical Science (P41GM103393).