One of the remaining "grand challenges" in chemistry is the development of a next generation, less expensive, cleaner process that can allow the vast reserves of methane from natural gas to augment or replace oil as the source of fuels and chemicals. Homogeneous (gas/liquid) systems that convert methane to functionalized products with emphasis on reports after 1995 are reviewed. Gas/solid, bioinorganic, biological, and reaction systems that do not specifically involve methane functionalization are excluded. The various reports are grouped under the main element involved in the direct reactions with methane. Central to the review is classification of the various reports into 12 categories based on both practical considerations and the mechanisms of the elementary reactions with methane. Practical considerations are based on whether or not the system reported can directly or indirectly utilize O as the only net coreactant based only on thermodynamic potentials. Mechanistic classifications are based on whether the elementary reactions with methane proceed by chain or nonchain reactions and with stoichiometric reagents or catalytic species. The nonchain reactions are further classified as CH activation (CHA) or CH oxidation (CHO). The bases for these various classifications are defined. In particular, CHA reactions are defined as elementary reactions with methane that result in a discrete methyl intermediate where the formal oxidation state (FOS) on the carbon remains unchanged at -IV relative to that in methane. In contrast, CHO reactions are defined as elementary reactions with methane where the carbon atom of the product is oxidized and has a FOS less negative than -IV. This review reveals that the bulk of the work in the field is relatively evenly distributed across most of the various areas classified. However, a few areas are only marginally examined, or not examined at all. This review also shows that, while significant scientific progress has been made, greater advances, particularly in developing systems that can utilize O, will be required to develop a practical process that can replace the current energy and capital intensive natural gas conversion process. We believe that this classification scheme will provide the reader with a rapid way to identify systems of interest while providing a deeper appreciation and understanding, both practical and fundamental, of the extensive literature on methane functionalization. The hope is that this could accelerate progress toward meeting this "grand challenge."