In the last a few decades, various puzzles have emerged in the study of strongly-correlated materials.  In a family strongly-correlated insulators, which are known as Kondo insulators, one such long-standing puzzle has remained open for over thirty years. Early transport data indicates that some Kondo insulators (e.g. SmB$_6$) display strange electrical transport that cannot be understood if one assumes that it is governed by the three-dimensional (3D) bulk. In this talk, I show that some Kondo insulators have the right ingredients to be topological insulators, which we called topological Kondo insulators. This topological picture opens up a new way to understand the strange transport behaviors for some of the Kondo insulators. I will also discuss the recent experiments, which indicates that SmB$_6$ is indeed a bulk insulator with a conducting surface.