Quantum spin liquids represent exotic states of matter. They do not order down to the lowest of temperatures but are characterized by long range entanglement and fractionalized excitations. While much is known about their behaviour in closed quantum system, their fate in the presence of coupling to environment remains less studied. The goal of this thesis is to investigate spin liquids in open as well as non-hermitian quantum systems. By starting from Kitaev's honeycomb lattice model, various couplings to environment will be considered and steady state of the system will be investigated. Among the physical quantities of interest, the topological entanglement entropy and spin correlation functions will be evaluated. Other models of spin liquids will also be studied in the presence of non-hermitian terms.