Quantum spin liquids are systems of interacting spins that do not magnetically order even at absolute zero. However they are not necessarily ordinary paramagnets -- it is here that we may see, even in table-top setups, highly unusual and unexpected phenomena. For example in an insulator consisting of localized spin-1/2 degrees of freedom, the lowest-lying excitations may be best described as free Majorana fermions! Excitations in some spin liquids in two dimensions could even be anyons -- particles that that do not obey Bose or Fermi statistics upon interchange of labels. Apart from the fundamental interest, these systems also hold the promise of future applications, such as the realization of qubits for the purpose of quantum computing.

The spin-1/2 honeycomb lattice Kitaev model provides a very appealing playground in this context. But realization of Kitaev physics in material systems has proved quite challenging. In this talk after giving broad overview of quantum spin liquids I will discuss fascinating aspects of Kitaev model,related experimental challanges and our recent work on Kitaev spin-liquid phase.