Realizing the Kitaev spin liquid in solid state systems has become one of the major goals of strongly correlated electron community.

I will introduce the background and some recent progresses on the iridium-based "Kitaev materials".

The development along this line poses serious challenges to theorists, on the accurate determination of the effective spin models for these materials

and the accurate computation of the properties of these "Kitaev+..." models.

I will describe some of our efforts in this direction.