Ever since Robert Hooke's 17th century discovery of the cell using a humble compound microscope, light-matter interactions have continuously redefined our understanding of cell biology. Fluorescence microscopy has been particularly transformative and remains an indispensable tool for many cell biologists. The subcellular localization of biomolecules is now routinely visualized simply by manipulating the wavelength of light. Fluorescence polarization microscopy (FPM) extends these capabilities by exploiting another optical property - polarization - allowing researchers to measure not only the location of molecules, but also their organization or alignment within larger cellular structures. With only minor modifications to an existing fluorescence microscope, FPM can reveal the nanoscale architecture, orientational dynamics, conformational changes and interactions of fluorescently labeled molecules in their native cellular environments. Importantly, FPM excels at imaging systems that are challenging to study through traditional structural approaches, such as membranes, membrane proteins, cytoskeletal networks and large macromolecular complexes. In this Review, we discuss key discoveries enabled by FPM, compare and contrast the most common optical setups for FPM, and provide a theoretical and practical framework for researchers to apply this technique to their own research questions.