Supersymmetry (SUSY) has been widely applied to nonrelativistic quantum mechanical problems in the past decade, leading to a deeper understanding of analytically solvable potentials and new approximation methods. This review discusses the theoretical formulation of SUSY quantum mechanics (SUSY QM) and its applications. Exactly solvable potentials are understood through concepts like supersymmetric partner potentials, shape invariance, and operator transformations. Many familiar solvable potentials exhibit shape invariance. New exactly solvable shape invariant potentials, including self-similar potentials, are described. The connection between inverse scattering, isospectral potentials, and SUSY QM is discussed, along with multi-soliton solutions of the KdV equation. Approximation methods within SUSY QM are also covered, showing that a SUSY-inspired WKB approximation is exact for shape invariant potentials. SUSY ideas yield particularly useful results for tunneling rates in double well potentials and for improving large N expansions. The paper also discusses a charged Dirac particle in an external magnetic field and other potentials using SUSY QM. It explores structures beyond SUSY QM, such as parasupersymmetric quantum mechanics, where there is a symmetry between a boson and a para-fermion of order p. The article covers various topics, including the Hamiltonian formulation of SUSY QM, factorization and the hierarchy of Hamiltonians, shape invariance and solvable potentials, operator transforms, the SUSY WKB approximation, isospectral Hamiltonians, path integrals, perturbative methods, the Pauli equation, the Dirac equation, singular superpotentials, and parasupersymmetric quantum mechanics. It also discusses the implications of SUSY for the hierarchy problem, the role of SUSY in quantum field theories, and the connection between SUSY and stochastic processes. The paper concludes with a discussion of the importance of SUSY in quantum mechanics and its broader implications in physics.Supersymmetry (SUSY) has been widely applied to nonrelativistic quantum mechanical problems in the past decade, leading to a deeper understanding of analytically solvable potentials and new approximation methods. This review discusses the theoretical formulation of SUSY quantum mechanics (SUSY QM) and its applications. Exactly solvable potentials are understood through concepts like supersymmetric partner potentials, shape invariance, and operator transformations. Many familiar solvable potentials exhibit shape invariance. New exactly solvable shape invariant potentials, including self-similar potentials, are described. The connection between inverse scattering, isospectral potentials, and SUSY QM is discussed, along with multi-soliton solutions of the KdV equation. Approximation methods within SUSY QM are also covered, showing that a SUSY-inspired WKB approximation is exact for shape invariant potentials. SUSY ideas yield particularly useful results for tunneling rates in double well potentials and for improving large N expansions. The paper also discusses a charged Dirac particle in an external magnetic field and other potentials using SUSY QM. It explores structures beyond SUSY QM, such as parasupersymmetric quantum mechanics, where there is a symmetry between a boson and a para-fermion of order p. The article covers various topics, including the Hamiltonian formulation of SUSY QM, factorization and the hierarchy of Hamiltonians, shape invariance and solvable potentials, operator transforms, the SUSY WKB approximation, isospectral Hamiltonians, path integrals, perturbative methods, the Pauli equation, the Dirac equation, singular superpotentials, and parasupersymmetric quantum mechanics. It also discusses the implications of SUSY for the hierarchy problem, the role of SUSY in quantum field theories, and the connection between SUSY and stochastic processes. The paper concludes with a discussion of the importance of SUSY in quantum mechanics and its broader implications in physics.