The use of Graphene based materials, such as graphene oxide (GO), in biosensing applications is gaining significant interest, due to high signal output, with strong potential for high industrial growth rate. Graphene's excellent conduction and mechanical properties (such as toughness and elasticity) coupled with high reactivity to chemical molecules are some of its appealing properties. The presence of ripples on the surface (whether indigenous or induced) represents another property/variable that provide enormous potential if harnessed properly. In this article, we review the current knowledge regarding the use of graphene for biosensing. We discuss briefly the general topic of using graphene for biosensing applications with special emphasis on wearable graphene-based biosensors. The intrinsic ripples of graphene and their effect on graphene biosensing capabilities are thoroughly discussed. We dedicate a section also for the manipulation of intrinsic ripples. Then we review the use of Graphene oxide (GO) in biosensing and discuss the effect of ripples on its properties. We present a review of the current biosensor devices made out of GO for detection of different molecular targets. Finally, we present some thoughts for future perspectives and opportunities of this field. STATEMENT OF SIGNIFICANCE: Biosensors are tools that detect the presence and amount of a chemical substance, such as pregnancy tests and glucose monitoring devices. They are general portable, have short response times and are sensitive, making them highly effective. Gold and silver are used in biosensors and more recently, graphene. Graphene is sheets of carbon atoms and is the only two-dimensional crystal in nature. It has unique features allowing its effective use in biosensing applications, including the presence of ripples (non-flat areas that give it its electronic properties). The last comprehensive review of this topic was published in 2016. This paper reviews the current knowledge of graphene based biosensors, with a focus on ripples and their effect on graphene biosensing capabilities.