Heterogeneities in two-dimensional (2D) materials, including variations in layer number and stacking order, spatial variations in chemical composition, and point defects, may provide these systems with a variety of unique optical and electronic properties. Many of these structures form inherently when 2D materials are produced on a large scale with chemical vapor deposition (CVD), and artificial heterojunctions between different 2D materials can also be produced by design. In this work, we address the challenges of visualizing the local structure and composition of heterogeneous 2D materials, and of establishing clear relationships between these structural features and the materials' properties. For this purpose, we first introduce two novel optical imaging spectroscopy techniques: DUV-Vis-NIR hyperspectral microscopy and widefield Raman imaging. These techniques enable comprehensive, all-optical mapping of chemical composition in lateral 2D heterojunctions, graphene visualization on arbitrary substrates, large-scale studies of defect distribution in CVD-grown samples, and real-time imaging of dynamic processes. They can also determine the optical response of an unknown 2D material, and in combination with existing high resolution imaging tools such as dark-field transmission electron microscopy, they can be used to establish quantitative structure-property relationships for a variety of 2D heterostructures. We next apply these methods to the first comprehensive study of the optical properties of twisted bilayer graphene (tBLG), a heterostructure where two graphene layers are rotated by a relative angle ([theta]), relating the optical conductivity and Raman spectra to [theta] for many tBLG samples. Our results establish the importance of interlayer coupling in tBLG at all [theta], and our data suggest that unique many-body effects play vital roles in both the optical absorption and Raman response of tBLG. These findings provide a framework for understanding the effects of the [theta] degree of freedom in other stacked 2D materials, and the suite of techniques that we have developed will play a key role in the characterization of heterogeneous 2D materials for years to come.