This review discusses the theory of Majorana zero modes (MZMs) in unconventional superconductors. Majorana fermions, initially proposed by Ettore Majorana, are their own antiparticles and have been studied in both particle physics and condensed matter physics. In condensed matter, MZMs emerge as zero-energy quasiparticles in superconductors, particularly in topological superconductors. These quasiparticles exhibit unique properties such as charge neutrality, spin-polarization, and spatial nonlocality. The review emphasizes the emergence of MZMs as self-conjugated zero-energy surface Andreev bound states (ZESABSs) at the boundaries of unconventional superconductors. It explores their formation in one-dimensional spin-polarized p-wave superconductors, where they appear as zero-energy edge states. The review also discusses the analytical derivation of Green's functions for p-wave superconductors, showing that MZMs are accompanied by odd-frequency spin-triplet pairing. The review highlights experimental signatures of MZMs, including zero-bias conductance peaks (ZBCPs) and the anomalous proximity effect. It also discusses the relationship between MZMs and topological superconductivity, emphasizing their potential for quantum computing applications. The review covers the formation of ZESABSs in various superconductors, including spin-triplet p-wave and spin-singlet d-wave superconductors, and their implications for topological invariants and quantum computing. The review concludes with a discussion of the challenges in detecting MZMs and the potential for future experimental verification.This review discusses the theory of Majorana zero modes (MZMs) in unconventional superconductors. Majorana fermions, initially proposed by Ettore Majorana, are their own antiparticles and have been studied in both particle physics and condensed matter physics. In condensed matter, MZMs emerge as zero-energy quasiparticles in superconductors, particularly in topological superconductors. These quasiparticles exhibit unique properties such as charge neutrality, spin-polarization, and spatial nonlocality. The review emphasizes the emergence of MZMs as self-conjugated zero-energy surface Andreev bound states (ZESABSs) at the boundaries of unconventional superconductors. It explores their formation in one-dimensional spin-polarized p-wave superconductors, where they appear as zero-energy edge states. The review also discusses the analytical derivation of Green's functions for p-wave superconductors, showing that MZMs are accompanied by odd-frequency spin-triplet pairing. The review highlights experimental signatures of MZMs, including zero-bias conductance peaks (ZBCPs) and the anomalous proximity effect. It also discusses the relationship between MZMs and topological superconductivity, emphasizing their potential for quantum computing applications. The review covers the formation of ZESABSs in various superconductors, including spin-triplet p-wave and spin-singlet d-wave superconductors, and their implications for topological invariants and quantum computing. The review concludes with a discussion of the challenges in detecting MZMs and the potential for future experimental verification.