MgB2 is a relatively new superconductor; it has attracted great interest from superconductor researchers all over the world. Thorough investigations have been carried out to study the material fabrication, as well as to study the material and superconducting properties from a fundamental physics point of view. The University of Wollongong has played a very active role in this research and a leading role in the research on high critical current density and high critical magnetic fields. Our recent research on the improvement of critical current density and the upper critical magnetic field by carbon-based compound doping is reviewed in this paper. It has absorbed great interest from superconductor researchers all over the world. Thorough investigations have been carried out to study the material fabrication, as well as to study the material and superconducting properties from a fundamental physics point of view. The University of Wollongong has played a very active role in this research and a leading role in the research on high critical current density and high critical magnetic fields. Our recent research on the improvement of critical current density and the upper critical magnetic field by carbon- based compound doping is reviewed in this paper.