<p>Non-Fourier heat conduction models are extended in response to heat transfer phenomena that cannot be accurately described by Fourier’s Law of heat conduction. This paper provides a review of heat conduction in functionally graded materials (FGMs) employing non-Fourier models. FGMs are designed materials with a gradual transition in composition, microstructure, or thermal conductivity throughout their volume. The spatial variation in thermal conductivity can lead to deviations from Fourier’s Law, resulting in non-Fourier heat conduction behavior in certain situations, such as at very short time scales or in materials with high thermal conductivity gradients. Researchers utilized various models, such as, Cattaneo-Vernotte, parabolic two-step model, hyperbolic two-step, phonon kinetic, dual-phase lag, and three-phase lag models to describe non-Fourier heat conduction phenomena. The objective of this review is to enhance the understanding of non-Fourier heat transfer in FGMs. As a result, the analytical studies conducted in this particular area receive a greater emphasis and focus. Various factors affecting non-Fourier heat conduction in FGMs including gradient function, material gradient index, initial conditions, boundary conditions, and type of non-Fourier model are investigated in various geometries. The literature reviews reveal that a significant portion of research efforts is centered around the utilization of dual phase lag and hyperbolic models in the field of non-Fourier heat conduction within FGMs.</p>