This paper explores the Theoretical and Experimental Studies of Majorana Fermions.Majorana fermions, first proposed by Ettore Majorana in 1937, are particles that are their own antiparticles, challenging traditional particle physics frameworks. Theoretical studies have provided a foundation for understanding these unique particles, suggesting their potential existence in specific quantum systems such as topological superconductors and insulators. Majorana fermions are characterized by their self-conjugate nature, meaning they are indistinguishable from their antiparticles. This property has profound implications for both fundamental physics and practical applications. In theoretical models, Majorana fermions are predicted to emerge in materials with special electronic and topological properties. Topological superconductors, for instance, are anticipated to host Majorana zero modes—localized, zero-energy states that are associated with Majorana fermions. These predictions have driven significant experimental efforts to detect these elusive particles. Experimental studies have focused on identifying Majorana zero modes in various systems, including superconducting nanowires, quantum dots, and two-dimensional materials like graphene. Techniques such as scanning tunneling microscopy (STM) and spectroscopy are employed to probe these systems for the presence of Majorana modes. Recent experimental advances have reported results consistent with Majorana zero modes, although distinguishing these from other zero-energy states remains challenging. The search for Majorana fermions is also driven by their potential applications in quantum computing. Topological qubits based on Majorana fermions are proposed to offer enhanced error resistance, promising more stable and reliable quantum computations. As research progresses, both theoretical predictions and experimental investigations continue to refine our understanding of Majorana fermions, aiming to confirm their existence and explore their practical applications.