Graphene as a truly 2-dimensional (2D) system is a promising candidate material for various optoelectronic applications. Implementing graphene as the main building material in ultra-broadband photodetectors has been the center of extensive research due to its unique absorption spectrum which covers most of the electro-magnetic spectra. However, one of the main challenges facing the wide application of pure graphene photodetectors has been the small optical absorption of monolayer graphene. Although novel designs were proposed to overcome this drawback, they often need complicated fabrication processes in order to integrate with the graphene photodetector. In this regard, fabrication of purely graphene photodetectors is a promising approach towards the manufacturing of simple, inexpensive, and high photosensitive devices. The fabrication of full graphene photodetectors (FGPDs) is mainly based on obtaining an optimal technique for the growth of high quality graphene, modification of electronic and optical properties of the graphene, appropriate techniques for transfer of graphene from the grown substrate to the desire position, and a proper design for photodetection. Therefore, the available states of the art techniques for each step of device fabrication, along with their pros and cons, are reviewed and the possible approaches for optimization of FGPDs have been proposed.