Key words lead iodide structure, layered inorganic structures, viewing different polytypes Lead Iodide (PbI2) is an important inorganic solid for both basic scientific research and possible technological applications and in this brief review we discuss the structure of PbI2. Although the basic structure is a simple I-Pb-I layered structure with a [PbI6] 4-near-octahedron being the basic building block, there are many ways of stacking the layers which results in many polytypes. We present 20 of the 23 entries for the structure of PbI2 from the Inorganic Structural Database and order them by polytype. This represents more than 80 years of crystallographic research in the structure of this compound. We present a simple way to view the 2H, 4H, 6H, and 6R polytypes and extend the procedure to higher-order polytypes. We note a relationship, not generally appreciated, between the distortion of the near [PbI6] 4-octahedrons and the polytype. We suggest that the significance of vacancies has only recently been appreciated. We suggest that small discrepancies in structure determination are probably due to different distributions of vacancies and that there are, in practice, very many structures for macroscopic or even mesoscopic samples of a given polytype when vacancies are considered.