This review is focused on assessment of solvents for cellulose dissolution and the mechanism of regeneration of the dissolved biopolymer. The solvents of interest are imidazole-based ionic liquids, quaternary ammonium electrolytes, salts of super-bases, and their binary mixtures with molecular solvents. We briefly discuss the mechanism of cellulose dissolution and address the strategies for assessing solvent efficiency, as inferred from its physico-chemical properties. In addition to the favorable effect of lower cellulose solution rheology, microscopic solvent/solution properties, including empirical polarity, Lewis acidity, Lewis basicity, and dipolarity/polarizability are determinants of cellulose dissolution. We discuss how these microscopic properties are calculated from the UV-Vis spectra of solvatochromic probes, and their use to explain the observed solvent efficiency order. We dwell briefly on use of other techniques, in particular NMR and theoretical calculations for the same purpose. Once dissolved, cellulose is either regenerated in different physical shapes, or derivatized under homogeneous conditions. We discuss the mechanism of, and the steps involved in cellulose regeneration, via formation of mini-sheets, association into "mini-crystals", and convergence into larger crystalline and amorphous regions. We discuss the use of different techniques, including FTIR, X-ray diffraction, and theoretical calculations to probe the forces involved in cellulose regeneration.