This paper surveys on-shell and off-shell higher derivative supergravities in dimensions 1 ≤ D ≤ 11. It summarizes various approaches to their construction, including the Noether procedure, harmonic superspace, superform method, superconformal tensor calculus, S-matrix and dimensional reduction. The bosonic parts of the invariants and the supertransformations of the fermionic fields are provided. The process of going on-shell, solutions to the Killing spinor equations, typical supersymmetric solutions, and the role of duality symmetries in the context of R⁴, D⁴R⁴ and D⁶R⁴ invariants are reviewed. The paper discusses the construction of higher derivative supergravities in various dimensions, including D = 11, 10, 9, 8, 7, 6, 5, and lower dimensions. It covers the superspace approach, the Noether procedure, superconformal tensor calculus, harmonic superspace, superform method, and dimensional reduction. The paper also discusses the role of duality symmetries, the relevance of higher derivative terms in the low energy limit of string theory, and the implications for black hole physics, AdS/CFT correspondence, and cosmology. The paper also discusses the relevance of higher derivative corrections to supergravities in the context of holography, including their implications for conformal anomalies of the dual CFTs. It also discusses the applications of higher derivative supergravities in cosmology, including the possible shapes for non-gaussianity for gravitational waves in the de Sitter approximation. The paper concludes with a discussion of the motivations for constructing and studying higher derivative supergravities, including their relevance to the black hole entropy, their implications for the conformal anomalies of the dual CFTs, and their applications in cosmology. It also discusses the role of local supersymmetry and the attendant duality symmetries in the organization of the higher derivative terms in the low-energy effective action. The paper also discusses the criteria for UV completion of quantum gravity, including the requirements of unitarity and causality, and the relevance of higher derivative corrections to supergravities in the context of holography.This paper surveys on-shell and off-shell higher derivative supergravities in dimensions 1 ≤ D ≤ 11. It summarizes various approaches to their construction, including the Noether procedure, harmonic superspace, superform method, superconformal tensor calculus, S-matrix and dimensional reduction. The bosonic parts of the invariants and the supertransformations of the fermionic fields are provided. The process of going on-shell, solutions to the Killing spinor equations, typical supersymmetric solutions, and the role of duality symmetries in the context of R⁴, D⁴R⁴ and D⁶R⁴ invariants are reviewed. The paper discusses the construction of higher derivative supergravities in various dimensions, including D = 11, 10, 9, 8, 7, 6, 5, and lower dimensions. It covers the superspace approach, the Noether procedure, superconformal tensor calculus, harmonic superspace, superform method, and dimensional reduction. The paper also discusses the role of duality symmetries, the relevance of higher derivative terms in the low energy limit of string theory, and the implications for black hole physics, AdS/CFT correspondence, and cosmology. The paper also discusses the relevance of higher derivative corrections to supergravities in the context of holography, including their implications for conformal anomalies of the dual CFTs. It also discusses the applications of higher derivative supergravities in cosmology, including the possible shapes for non-gaussianity for gravitational waves in the de Sitter approximation. The paper concludes with a discussion of the motivations for constructing and studying higher derivative supergravities, including their relevance to the black hole entropy, their implications for the conformal anomalies of the dual CFTs, and their applications in cosmology. It also discusses the role of local supersymmetry and the attendant duality symmetries in the organization of the higher derivative terms in the low-energy effective action. The paper also discusses the criteria for UV completion of quantum gravity, including the requirements of unitarity and causality, and the relevance of higher derivative corrections to supergravities in the context of holography.