Understanding thermal energy transport of crystalline materials, often highly dependent on their crystalline directions, is crucial for energy harvesting and thermal management applications. In this sense, anisotropy in thermal conductivity (<i>κ</i>), which is the unique characteristic of two-dimensional (2D) materials involving graphene and transition metal dichalcogenides (TMDs), has been attracting tremendous attention in terms of fundamental science and application-driven technology aspects. This distinctive heat transport behavior of 2D van der Waals (vdW) materials generally originates from their intrinsic crystal structures and associated lattice vibrations. Here, we thoroughly review and summarize the anisotropic thermal conductivity in 2D vdW crystals in two different categories: 1) in-plane vs. out-of-plane and 2) between two different in-plane directions. In addition, we introduce a range of thermal conductivity measurement techniques that can be employed for 2D vdW materials provided with their working principles, advantages, and limitations. Beyond their intrinsic anisotropic ratio, we conclude with perspectives on the extrinsic modulations of thermal conductivities, thereby maximizing it toward effective thermal management.