Recently, graphene has been extensively researched in fundamental science and engineering fields and has been developed for various electronic applications in emerging technologies owing to its outstanding material properties, including superior electronic, thermal, optical and mechanical properties. Thus, graphene has enabled substantial progress in the development of the current electronic systems. Here, we introduce the most important electronic and thermal properties of graphene, including its high conductivity, quantum Hall effect, Dirac fermions, high Seebeck coefficient and thermoelectric effects. We also present up-to-date graphene-based applications: optical devices, electronic and thermal sensors, and energy management systems. These applications pave the way for advanced biomedical engineering, reliable human therapy, and environmental protection. In this review, we show that the development of graphene suggests substantial improvements in current electronic technologies and applications in healthcare systems.