Realizing Majorana zero modes in superconductor-semiconductor heterostructures is a major goal in condensed matter physics. This review discusses recent progress in semiconductor-superconductor proposals for topological superconductivity, focusing on material science advancements and experimental signatures of Majorana zero modes (MZMs). The paper outlines next-generation experiments probing exotic properties of MZMs, including fusion rules and non-Abelian exchange statistics, and discusses prospects for implementing MZMs in topological quantum computing. Majorana zero modes are exotic neutral excitations in superconductors, which are their own antiparticles. They arise from the particle-hole symmetry of superconductors and lead to a massive ground-state degeneracy, which is essential for topological quantum computing. Theoretical predictions suggest that MZMs obey non-Abelian exchange statistics, making them promising for quantum gate operations. Experimental evidence for MZMs in proximitized nanowires has grown, with recent studies showing robust signatures such as zero-bias conductance peaks and Coulomb blockade effects. The paper discusses the key requirements for realizing MZMs, including strong spin-orbit coupling in semiconductors and high-quality superconducting interfaces. It reviews material science advancements in growing high-mobility semiconductors and preparing high-quality interfaces between superconductors and semiconductors. The review also covers the growth of nanowires using bottom-up Vapor-Liquid-Solid (VLS) techniques and the challenges of achieving controlled nanowire definitions. Superconducting interfaces are crucial for inducing superconductivity in semiconductors. The paper discusses the importance of minimizing disorder at the semiconductor/superconductor interface and the role of epitaxial growth in achieving high-quality interfaces. It also highlights the importance of controlling the superconducting gap and the role of magnetic fields in tuning the topological phase. The review discusses experimental signatures of MZMs, including zero-bias tunneling conductance measurements and Coulomb blockade experiments. These experiments provide evidence for the presence of MZMs and their non-local nature. The paper also discusses the importance of high-quality materials and improved device control in studying subtle transport properties of MZMs. Overall, the review highlights the progress in realizing MZMs in superconductor-semiconductor heterostructures and their potential for topological quantum computing. The paper emphasizes the importance of material science advancements in achieving high-quality interfaces and controlling the superconducting gap, which are essential for observing MZMs and their exotic properties.Realizing Majorana zero modes in superconductor-semiconductor heterostructures is a major goal in condensed matter physics. This review discusses recent progress in semiconductor-superconductor proposals for topological superconductivity, focusing on material science advancements and experimental signatures of Majorana zero modes (MZMs). The paper outlines next-generation experiments probing exotic properties of MZMs, including fusion rules and non-Abelian exchange statistics, and discusses prospects for implementing MZMs in topological quantum computing. Majorana zero modes are exotic neutral excitations in superconductors, which are their own antiparticles. They arise from the particle-hole symmetry of superconductors and lead to a massive ground-state degeneracy, which is essential for topological quantum computing. Theoretical predictions suggest that MZMs obey non-Abelian exchange statistics, making them promising for quantum gate operations. Experimental evidence for MZMs in proximitized nanowires has grown, with recent studies showing robust signatures such as zero-bias conductance peaks and Coulomb blockade effects. The paper discusses the key requirements for realizing MZMs, including strong spin-orbit coupling in semiconductors and high-quality superconducting interfaces. It reviews material science advancements in growing high-mobility semiconductors and preparing high-quality interfaces between superconductors and semiconductors. The review also covers the growth of nanowires using bottom-up Vapor-Liquid-Solid (VLS) techniques and the challenges of achieving controlled nanowire definitions. Superconducting interfaces are crucial for inducing superconductivity in semiconductors. The paper discusses the importance of minimizing disorder at the semiconductor/superconductor interface and the role of epitaxial growth in achieving high-quality interfaces. It also highlights the importance of controlling the superconducting gap and the role of magnetic fields in tuning the topological phase. The review discusses experimental signatures of MZMs, including zero-bias tunneling conductance measurements and Coulomb blockade experiments. These experiments provide evidence for the presence of MZMs and their non-local nature. The paper also discusses the importance of high-quality materials and improved device control in studying subtle transport properties of MZMs. Overall, the review highlights the progress in realizing MZMs in superconductor-semiconductor heterostructures and their potential for topological quantum computing. The paper emphasizes the importance of material science advancements in achieving high-quality interfaces and controlling the superconducting gap, which are essential for observing MZMs and their exotic properties.