Combustion limits and related flame behaviors are reviewed, especially with regard to fundamental problems. As for premixed flames, after a brief historical overview of research on the flammability limit, recent trends of research on planar propagating flames, curved propagating flames, flame balls, and stretched premixed flames are discussed, and then all types of flames are summarized. Finally, instability and dynamics near limits is discussed. With regard to combustion limits of counterflow diffusion flames and droplet flames, their instability is demonstrated, then an explanation of lifted flames and edge flames is presented. Suggestions for future work are also discussed in the concluding remarks. There are 166 references cited in this review article.