Mpemba effect is a counter-intuitive relaxation phenomenon where an initially prepared hotter system equilibrates faster than the one prepared at a lower temperature. Although common sense suggests that the colder one should equilibrate faster, this is an apparent paradox that goes back to the time of Aristotle, Rene Descartes, and Sir Francis Bacon. The effect was first discovered in the case of water, where it is described in terms of temperature as a measure. However, it turns out the effect is more general and can be studied in the context of relaxation dynamics in non-equilibrium systems. In this talk, we describe the Mpemba effect in two such systems namely driven granular gases and a colloidal Langevin system. The two examples provide a strong interplay between theory and experiment and can render a better understanding of the existence of the Mpemba effect. An exact analysis determining the criteria for the existence of the Mpemba effect in both systems will be presented. We will underpin the role of anisotropy in the kinetic energies and the presence of metastable states in the energy landscape that cause this counter-intuitive relaxation.