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This thesis presents an exact theoretical study of dynamical correlation functions in different phases of a two-dimensional quantum spin liquid. By calculating the dynamical spin structure factor and the Raman scattering cross section, this thesis shows that there are salient signatures-qualitative and quantitative-of the Majorana fermions and the gauge fluxes emerging as effective degrees of freedom in the exactly solvable Kitaev honeycomb lattice model. The model is a representative of a class of spin liquids with Majorana fermions coupled to Z2 gauge fields. The qualitative features of the response functions should therefore be characteristic for this broad class of topological states.