This paper investigates second-order viscous hydrodynamics in conformal field theories at finite temperature, focusing on the constraints imposed by conformal invariance. The authors show that conformal symmetry significantly restricts the form of second-order corrections to hydrodynamic equations. By matching these corrections to AdS/CFT calculations and recent results for Bjorken flow, they determine three of the five second-order transport coefficients in the strongly coupled N = 4 supersymmetric Yang-Mills theory. They also discuss how these coefficients can arise in the kinetic theory of weakly coupled conformal plasmas. The paper highlights that the Müller-Israel-Stewart theory, commonly used in numerical simulations, does not include all allowed second-order terms and often misses terms required by conformal invariance. The paper is structured into seven sections, starting with an introduction to relativistic hydrodynamics and its relevance in heavy-ion physics, astrophysics, and cosmology. It then explores the implications of conformal invariance for hydrodynamics, including Weyl anomalies and the first-order hydrodynamic equations. The second-order hydrodynamics of a conformal fluid is analyzed, with a focus on the second-order terms and their relation to transport coefficients. The paper then computes three of the five second-order transport coefficients for the N = 4 SYM theory using AdS/CFT correspondence. It also discusses the limitations of the Müller-Israel-Stewart theory and compares the results with those from kinetic theory. The paper concludes with a summary of the findings and their implications for the study of strongly coupled plasmas. Appendices provide additional details on the perturbative solutions of the shear and sound mode equations.This paper investigates second-order viscous hydrodynamics in conformal field theories at finite temperature, focusing on the constraints imposed by conformal invariance. The authors show that conformal symmetry significantly restricts the form of second-order corrections to hydrodynamic equations. By matching these corrections to AdS/CFT calculations and recent results for Bjorken flow, they determine three of the five second-order transport coefficients in the strongly coupled N = 4 supersymmetric Yang-Mills theory. They also discuss how these coefficients can arise in the kinetic theory of weakly coupled conformal plasmas. The paper highlights that the Müller-Israel-Stewart theory, commonly used in numerical simulations, does not include all allowed second-order terms and often misses terms required by conformal invariance. The paper is structured into seven sections, starting with an introduction to relativistic hydrodynamics and its relevance in heavy-ion physics, astrophysics, and cosmology. It then explores the implications of conformal invariance for hydrodynamics, including Weyl anomalies and the first-order hydrodynamic equations. The second-order hydrodynamics of a conformal fluid is analyzed, with a focus on the second-order terms and their relation to transport coefficients. The paper then computes three of the five second-order transport coefficients for the N = 4 SYM theory using AdS/CFT correspondence. It also discusses the limitations of the Müller-Israel-Stewart theory and compares the results with those from kinetic theory. The paper concludes with a summary of the findings and their implications for the study of strongly coupled plasmas. Appendices provide additional details on the perturbative solutions of the shear and sound mode equations.