With the demand for anticipated green hydrogen and power production, novel and upgraded catalytic processes are desired for more effective utilization of precious natural resources. Methane steam reforming is an advanced and matured technology for converting methane to hydrogen and syngas. As a renewable energy resource containing a large amount of methane, biogas is a promising fuel for green hydrogen production. Because of the fuel flexibility and high efficiency relative to alternative technologies, solid oxide fuel cells with internal methane reforming capabilities may become an economically viable technology for hydrogen and power generation. A renewed interest in the flexible application of biogas in solid oxide fuel cells for the co-generation of green hydrogen and power has emerged recently, driven by the spectacular advances in fuel cell technology. However, the methane reforming process suffers from inaccurate or unprecise descriptions. Knowledge of the factors influencing the reforming reaction rate on the novel and improved reforming anode catalysts in solid oxide fuel cells are still required to design and operate such systems. Therefore, a comprehensive review of recent advances in methane steam reforming provides meaningful insight into technological progress. Herein, major descriptors of the methane steam reforming reaction engineering are reviewed to provide a practical perspective for the direct application of biogas in solid oxide fuel cells, which serves as an alternative sustainable, flexible process for green hydrogen and power co-production. Current advances and challenges are evaluated, and perspectives for future work are discussed.