As the foundation of the next-generation Digital Earth, Discrete Global Grid Systems (DGGS) have demonstrated both theoretical and practical development, with a variety of state-of-the-art implementations proposed. These emerging DGGS platforms or libraries support preliminary operations such as quantization, cell-level navigation, and conversion between cell addresses and geographical coordinates, while leaving the other more complicated functions unexplored. This paper discusses the functional operations in a DGGS environment, including the essential operations defined by the Open Geospatial Consortium (OGC) Abstract Specification, and the extended operations potentially supported by DGGS. The extended operations are discussed in comparison to the traditional GIS, from the aspects of database techniques, data pre-processing and manipulation, spatial analysis and data interpretation, data computation, and data visualization. It was found that with the OGC-required operations and pre-processing operations as the baseline of development, some function algorithms can facilitate the algorithm development of other analytical functions. Several future research directions regarding the data modeling uncertainties, extended analytic algorithm development, and database and computation technologies are presented. This paper provides a comparison between DGGS and traditional GIS operations and can serve as a reference for future DGGS operation development.