In recent years, a number of data structures for global geo-referenced data sets have been proposed based on regular, multi-resolution partitions of polyhedra. We present a survey of the most promising of such systems, which we call Geodesic Discrete Global Grid Systems (Geodesic DGGSs). We show that Geodesic DGGS alternatives can be constructed by specifying five substantially independent design choices: a base regular polyhedron, a fixed orientation of the base regular polyhedron relative to the Earth, a hierarchical spatial partitioning method defined symmetrically on a face (or set of faces) of the base regular polyhedron, a method for transforming that planar partition to the corresponding spherical/ellipsoidal surface, and a method for assigning point representations to grid cells. The majority of systems surveyed are based on the icosahedron, use an aperture 4 triangle or hexagon partition, and are either created directly on the surface of the sphere or by using an equal-area transformation. An exa...