Quantum Hall effect (QHE) is the hallmark of two dimensional conductors. This phenomenon generated immense amount of experimental and theoretical research, mostly on III-V based material systems, over the past three decades. QHE is not only significant in fundamental physics, but has a major application as the standard of resistance. The best accuracy in determining the resistance quantum is limited by the breakdown of the quantum Hall effect which is observed as the rapid rise of longitudinal resistivity along with the smearing of the quantized Hall plateaus. Breakdown itself is a long standing puzzle in the field, since the collection of the experimental findings can not be explained by any of the single theoretical models for the microscopic mechanism of the breakdown. Graphene, a relatively new but pervasive two dimensional conductor, is now boosting the QHE research again. A new type of QHE is discovered in graphene due to the relativistic charge carriers. In this talk, I will summarize our efforts on graphene research around topic of breakdown of the anomalous quantum Hall effect at high currents in monolayer graphene. Dr. Kaya is an experimental condensed matter physicist. He received his Ph.D degree in physics from Bilkent University in 1997. Later he worked at Max-Planck-Institute in Stuttgart between 97-99 and at Rowland Institute at Harvard University between 99-2003. Since 2003 he is a faculty member at Sabancı University. Some of his interest are transport phenomena in nanostructures, low temperature physics, nanofabrication and scanning tunneling microscopy.