As nanotechnology floods application areas like medicine, electronics, water remediation, space and textiles, just to name a few, some nanomaterials remain in the spotlight due to their fantastic properties and their incredible potential. Such is the case of the 2D, transparent, flexible, strong, carbon-based nanomaterial called graphene. Graphene consists of sp2 hybridized carbon arranged in a flat network packed in a honey-comb pattern, having thus mono-atomic thickness. Its isolation in 2004 opened the door to numerous investigations and its research is funded each year by governments, industries and academia worldwide. Due to its non-hydrophilic nature, some applications represent a challenge (particularly biological and medical applications), thus an oxygen/hydrogen-functionalized hydrophilic version of it has lately gained popularity, its name is graphene oxide. This document aims to review the synthesis methods of graphene, graphene oxide and reduced graphene oxide. A revision of the most important top-down and bottom-up methods is presented, focusing on chemical vapor deposition for the growth of graphene and the wet-chemical methods for the synthesis of graphene oxide and the reduction techniques available for reduced graphene oxide. We conclude by analyzing the current situation of graphene and graphene oxide production and the challenges that need to be tackled in order to meet the short-term demand of these nanomaterials for the promised applications.