Graphene is a new and exciting material that has attracted much attention in the last decade and is being extensively explored because of its properties, which have been described with so many superlatives. Production of graphene for large scale application is still a major challenge. Top-down graphene exfoliation methods from graphite, such as liquid-phase exfoliation which is promising because of low cost and high scalability potential will be briefly discussed. We also analyze the challenges and possibilities of using graphene as a nanofiller in polymer composites which has resulted in enhanced electrical, mechanical and thermal properties. In this review, we take a panoramic approach to give insight on the different aspects of graphene such as properties, graphite-based production methods and also examples of graphene application in polymer composites and which will be beneficial to both novice and experts.