The search for quantum spin liquid (QSL) physics has been long and storied, but alpha-RuCl3 and the iridates A2IrO3 have opened up the possibility of realizing a new family of "Kitaev" quantum spin liquids. The Kitaev honeycomb model is a highly anisotropic quadratic spin model that has an exact QSL ground state. We study the Kitaev model on a variety of 3D lattices with the goal of identifying characteristic signatures of its QSL phase. We use the exact solution to demonstrate several features of the Kitaev QSL both quantitative and qualitative. These include broad Raman spectra characteristic of the fractionalized excitations and rich momentum-dependent RIXS spectra. We discuss how these measurements can probe novel features of these QSL's. For example, topological surface modes accessible to Brillouin scattering, and Landau level peaks in Raman spectra on carefully strained honeycomb flakes. In addition, the technical underpinnings of these calculations are reviewed in detail. Specifically, the theoretical predictions are completed with considerations of the effects of perturbations, finite temperature studies, and careful analysis of the experimental excitations.