One of the long-standing open problems which recently attracted a lot of attention is understanding how a quantum spin liquid (QSL) state responds to various forms of disorder, such as dislocations, vacancies, impurities, and bond randomness, which are inevitable in real materials. It has been noted that quenched disorder on top of the quantum disordered strongly correlated spin state of a QSL can give rise to diverse and often puzzling behaviors. In my talk, I will focus on the impact of disorder on the properties of the Kitaev QSL, which is realized in a system of spin-1/2 at sites of a honeycomb lattice interacting via Ising-like frustrated nearest-neighbor exchange interactions. This model is exactly solvable, has a QSLground state, and is yet realistic. One of the most exciting features of the Kitaev QSL is the fractionalization of spin excitations into itinerant Majorana fermions and static Z2 fluxes. The fact that the Majorana fermions in the Kitaev model are non-interacting and that this remains true even in the presence of various types of quenched disorder, makes the Kitaev QSL an ideal setting for exploringnovel disorder-induced localization effects on a quantitative level. In this work, we consider three types of disorder in the Kitaev model: the bond disorder, the site disorder and the thermal disorder. I will also discuss the effect of disorder on the low-temperature behavior of the 5d-electron compound H3LiIr2O6, which has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. I will show that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of H3LiIr2O6.