Natural rubber, obtained almost exclusively from the Para rubber tree (Hevea brasiliensis), is a unique biopolymer of strategic importance that, in many of its most significant applications, cannot be replaced by synthetic rubber alternatives. Several pressing motives lead to the search for alternative sources of natural rubber. These include increased evidence of allergenic reactions to Hevea rubber, the danger that the fungal pathogen Microcyclus ulei, causative agent of South American Leaf Blight (SALB), might spread to Southeast Asia, which would severely disrupt rubber production, potential shortages of supply due to increasing demand and changes in land use, and a general trend towards the replacement of petroleum-derived chemicals with renewables. Two plant species have received considerable attention as potential alternative sources of natural rubber: the Mexican shrub Guayule (Parthenium argentatum Gray) and the Russian dandelion (Taraxacum koksaghyz). This review will summarize the current production methods and applications of natural rubber (dry rubber and latex), the threats to the production of natural rubber from the rubber tree, and describe the current knowledge of the production of natural rubber from guayule and Russian dandelion.