Quantum spin liquids can arise from Kitaev magnetic interactions, and exhibit fractionalized excitations with the potential for a topological form of quantum computation. This review surveys recent experimental and theoretical progress on the pursuit of phenomena related to Kitaev magnetism in layered and exfoliatable materials, which offer numerous opportunities to apply powerful techniques from the field of atomically thin materials. We primarily focus on the antiferromagnetic Mott insulator $\alpha$-RuCl3, which exhibits Kitaev couplings and is readily exfoliated to single- or few-layer sheets, and thus serves as a test bed for developing probes of Kitaev phenomena in atomically thin materials and devices. We introduce the Kitaev model and how it is realized in $\alpha$-RuCl3 and other material candidates; and cover $\alpha$-RuCl3 synthesis and fabrication into van der Waals heterostructure devices. A key discovery is a work-function-mediated charge transfer that heavily dopes both the $\alpha$-RuCl3 and proximate materials, and can enhance Kitaev interactions by up to 50%. We further discuss a wide range of recent results in electronic transport and optical and tunneling spectroscopies of $\alpha$-RuCl3 devices. The experimental techniques and theoretical insights developed for $\alpha$-RuCl3 establish a framework for discovering and engineering superior two-dimensional Kitaev materials that may ultimately realize elusive quantum spin liquid phases.