Abstract: Knowledge of how heat flows anisotropically in van der Waals (vdW) materials is crucial for thermal management of emerging 2D materials devices and design of novel anisotropic thermoelectric materials. Despite the importance, anisotropic heat transport in vdW materials is yet to be systematically studied and is often presumably attributed to anisotropic speeds of sound in vdW materials due to soft interlayer bonding relative to covalent in-plane networks of atoms. In this work, we investigate the origins of the anisotropic heat transport in vdW materials, through time-domain thermoreflectance (TDTR) measurements and first-principles calculations of anisotropic thermal conductivity of three different phases of MoTe2. MoTe2 is ideal for the study due to its weak anisotropy in the speeds of sound. We find that even when the speeds of sound are roughly isotropic, the measured thermal conductivity of MoTe2 along the c-axis is 5-8 times lower than that along the in-plane axes. We derive meaningful characteristic heat capacity, phonon group velocity, and relaxation times from our first principles calculations for selected vdW materials (MoTe2, BP, h-BN, and MoS2), to assess the contributions of these factors to the anisotropic heat transport. Interestingly, we find that the main contributor to the heat transport anisotropy in vdW materials is anisotropy in heat capacity of the dominant heat-carrying phonon modes in different directions, which originates from anisotropic optical phonon dispersion and disparity in the frequency of heat-carrying phonons in different directions. The discrepancy in frequency of the heat-carrying phonons also leads to similar to 2 times larger average relaxation times in the cross-plane direction, and partially explains the apparent dependence of the anisotropic heat transport on the anisotropic speeds of sound. This work provides insight into understanding of the anisotropic heat transport in vdW materials.