The review is devoted to the production of 2D graphene nanostructures (few-layer graphene) using the method of carbonization of biopolymers developed by the authors by self-propagating high-temperature synthesis (SHS). The work analyzed and generalized the experimental and some theoretical results obtained, on the basis of which a phenomenological model for the synthesis of 2D graphene structures by SHS process was proposed. The main focus is on results obtained over the past 10 years. Finally, the prospects for ongoing research on the carbonization of biopolymers are discussed. Particular attention is paid to areas of research that are expected to be of most interest for the practical use of few-layer graphene in the near future.