The efficiency of photosynthetic light energy conversion depends largely on the molecular architecture of the photosynthetic membranes. Linear- and circular-dichroism (LD and CD) studies have contributed significantly to our knowledge of the molecular organization of pigment systems at different levels of complexity, in pigment-protein complexes, supercomplexes, and their macroassemblies, as well as in entire membranes and membrane systems. Many examples show that LD and CD data are in good agreement with structural data; hence, these spectroscopic tools serve as the basis for linking the structure of photosynthetic pigment-protein complexes to steady-state and time-resolved spectroscopy. They are also indispensable for identifying conformations and interactions in native environments, and for monitoring reorganizations during photosynthetic functions, and are important in characterizing reconstituted and artificially constructed systems. This educational review explains, in simple terms, the basic physical principles, and theory and practice of LD and CD spectroscopies and of some related quantities in the areas of differential polarization spectroscopy and microscopy.