In this talk, I will discuss the story about solving a 40+ year mystery, in which experimental and theoretical groups in our department have been playing a critical role. In the study of strongly-correlated systems, a long-standing puzzle remained open for over 40 years. For some strongly-correlated heavy fermion insulators (e.g. SmB6), the electrical transport shows both insulating and conducting signature, and the strange electrical transport cannot be understood no matter whether we assume the material being an insulator or a metal. In this talk, I will discuss recent theoretical and experimental progress that indicates that SmB6 is a topological Kondo insulator. In contrast to an ordinary three-dimensional insulator, the two-dimensional surface of such a material is a topologically-protected 2D metal. As a result, the low-temperature transport of SmB6 is dominated by its 2D surface rather than the 3D bulk. This result offers a natural explanation for the long-standing puzzle mentioned above, and makes SmB6 the best candidate for the first ideal 3D topological insulator.