Graphene is a fascinating material with excellent electrical, optical, mechanical, and chemical properties. Remarkable progress has been made in the development of methods for synthesizing large-area, high-quality graphene. Recently, the chemical vapor deposition method has opened up the possibility of using graphene for electronic devices and other applications. This review covers simple and inexpensive methods to grow graphene using polymers as solid carbon sources; which do not require an additional process to transfer graphene from the growth substrate to the receiver substrate.