For the high transition temperature (Tc) and low cost taking both raw materials and fabrication process into account, MgB2 has been a competitive candidate to replace��the conventional NiTi superconductor for high-temperature application in fault current limiters, transformers, motors, magnetic resonance imaging, adiabatic demagnetization refrigerators, generators, etc. The carbon-containing materials addition induced high critical current density (Jc) is reviewed based on their influences on the upper critical field (Hc2), flux pinning force, and connectivity. The doping effects were compared in the overview focusing on SiC, organic dopants, and graphene-related dopants. SiC doping is featured for the high-field critical current density, which is caused by the increased Hc2 attributed to the substitution of carbon on boron site and the strong flux pinning force offered by the nanosized secondary phases in the MgB2 matrix. Organic dopants have the advantage over SiC dopant for their relatively homogeneous distribution in the MgB2 matrix based on wet mixing of the organics and the raw boron powders. Low doping level of two-dimensional materials can improve the superconducting properties in all measured fields because of the combined advantages of carbon substitution effect and grain connectivity. MgB2 fabricated with carbon-encapsulated boron also introduces strong flux pinning centers in MgB2, which show weak destruction of the connectivity of the MgB2 grains as reflected by the low-magnetic-supercurrent behavior. High-pressure treatment and diffusion method can fabricate high-density MgB2 superconductors with better connectivity and increase the Jc compared with the in situ and ex situ methods.