The interesting and tunable properties of layered metal dichalcogenides (MX₂) and other layered materials heavily depend on their phase and layer stacking. We discovered that chemical exfoliation of layered MX₂ nanosheets and simultaneous conversion from the semiconducting 2H polymorph to the metallic 1T polymorph grants greatly enhanced activity for electrocatalytic hydrogen evolution reaction (HER). We have also developed layer-controlled vertical heterostructures of MX₂ by van der Waals epitaxy that have strong electronic interactions across the heterojunctions. We explain how the layer stacking and physical properties of MX₂ are influenced by screw dislocations. A one-to-one correlation of atomic force microscopy and high- and low-frequency Raman spectroscopy of many dislocated WSe₂ nanoplates reveals variations in the number and shapes of dislocation spirals and different layer stackings that are determined by the number, rotation, and location of the dislocations. These lead to three class of behaviors: plates with triangular dislocation spirals have non-centrosymmetric stacking that gives rise to strong second-harmonic generation, plates with hexagonal dislocation spirals form the bulk 2H layer stacking commonly observed, and plates containing mixed dislocation shapes have intermediate non-centrosymmetric stackings with mixed properties. We also explain layer stackings also determine the etching behaviors of multilayer WSe2 materials that result in complex chemically derived kirigami structures.