This article complements those mentioned above by providing a pedagogical introduction to this subject and reviews the current status of the field. We explain, at an introductory level, why sophisticated approaches are needed to study QSL states, how these approaches are implemented in practice, and what new physics may be expected to appear. The experimental side of the story and the drawbacks or pitfalls of the theoretical approaches are also discussed. We concentrate mainly on spin $1/2$ systems and study in detail one particular set of plausible spin liquid states that are usually termed resonating valence bond (RVB) states. The spins are treated as fermions in these states, which may be viewed as an extension of Fermi liquid states to Mott insulators. They are usually classified in the category of $SU(2)$, $U(1)$ or $Z_2$ spin liquid states. Because of the intrinsic limitations of the fermionic RVB approach, many other approaches to spin liquid states have been developed by different authors. These approaches often lead to other exotic possibilities not covered by the simple fermionic approach. Two of these approaches are introduced in this article for completeness: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb 