This review provides an in-depth theoretical analysis of the electronic properties of graphene and bilayer graphene. Graphene, a two-dimensional sheet of carbon atoms, exhibits unique electronic behavior due to its massless Dirac fermion nature, leading to phenomena such as the quantum Hall effect and relativistic-like properties. Bilayer graphene, composed of two stacked monolayers, has a quadratic band structure and can be tuned to have a tunable band gap via a top gate. The review discusses the quantum Hall effect in both monolayer and bilayer graphene, highlighting differences in their electronic behavior. It also covers the role of electron-electron interactions, phonon anomalies, and electron-phonon coupling in graphene. The paper explores the transport properties of graphene in the absence of an external magnetic field, including the effects of disorder and the metal-insulator transition. It also addresses the confinement of electrons in graphene, the unique properties of graphene nanoribbons, and the influence of substrate interactions, adsorbates, and lattice defects on the band structure. The review highlights the potential of graphene and bilayer graphene in various applications, including spintronic devices, single-molecule sensors, and transistors. The paper also discusses the manipulation of the band gap and magnetic properties of graphene through doping, adsorption, and lattice modifications. Overall, the review provides a comprehensive overview of the theoretical and experimental studies on graphene and bilayer graphene, emphasizing their unique electronic and transport properties.This review provides an in-depth theoretical analysis of the electronic properties of graphene and bilayer graphene. Graphene, a two-dimensional sheet of carbon atoms, exhibits unique electronic behavior due to its massless Dirac fermion nature, leading to phenomena such as the quantum Hall effect and relativistic-like properties. Bilayer graphene, composed of two stacked monolayers, has a quadratic band structure and can be tuned to have a tunable band gap via a top gate. The review discusses the quantum Hall effect in both monolayer and bilayer graphene, highlighting differences in their electronic behavior. It also covers the role of electron-electron interactions, phonon anomalies, and electron-phonon coupling in graphene. The paper explores the transport properties of graphene in the absence of an external magnetic field, including the effects of disorder and the metal-insulator transition. It also addresses the confinement of electrons in graphene, the unique properties of graphene nanoribbons, and the influence of substrate interactions, adsorbates, and lattice defects on the band structure. The review highlights the potential of graphene and bilayer graphene in various applications, including spintronic devices, single-molecule sensors, and transistors. The paper also discusses the manipulation of the band gap and magnetic properties of graphene through doping, adsorption, and lattice modifications. Overall, the review provides a comprehensive overview of the theoretical and experimental studies on graphene and bilayer graphene, emphasizing their unique electronic and transport properties.