In the study of strongly-correlated insulators, a long-standing puzzle remained open for over 40 years.Some Kondo insulators (or mixed-valent insulators) display strange electrical transport that cannot be understood if one assumes that it is governed by the three-dimensional bulk.In this talk, I show that some 3D Kondo insulators have the right ingredients to be topological insulators, which we called "topological Kondo insulators".