Currently, polymers are competing with metals and ceramics to realize various material characteristics, including mechanical and electrical properties. However, most polymers consist of organic matter, making them vulnerable to flames and high-temperature conditions. In addition, the combustion of polymers consisting of different types of organic matter results in various gaseous hazards. Therefore, to minimize the fire damage, there has been a significant demand for developing polymers that are fire resistant or flame retardant. From this viewpoint, it is crucial to design and synthesize thermally stable polymers that are less likely to decompose into combustible gaseous species under high-temperature conditions. Flame retardants can also be introduced to further reinforce the fire performance of polymers. In this review, the combustion process of organic matter, types of flame retardants, and common flammability testing methods are reviewed. Furthermore, the latest research trends in the use of versatile nanofillers to enhance the fire performance of polymeric materials are discussed with an emphasis on their underlying action, advantages, and disadvantages.