Lattice vibrations are the microscopic mechanism responsible for a large, if not dominant, contribution to heat transport in crystalline insulators. These vibrations are described in terms of phonons, collective excitations (or quasiparticles) in the form of waves of atomic displacements inside a crystal. Phonons are traditionally considered to be the quasiparticles responsible for carrying heat through the material. Heat transport is considered as a flux of a phonon gas, diffusing from hot areas (high phonon densities) to cold areas (low phonon densities) in an attempt to reestablish equilibrium, with phonon collisions being the source of heat flux dissipation. However, as dimensionality is reduced, the motion of phonons stimulated by temperature perturbations becomes correlated and this gas-like picture of thermal transport in terms of phonons becomes invalid. In this Thesis, we lay out an interpretation of thermal transport in 2D materials based on the Boltzmann transport equation in the form of collective excitations of phonons. These collective phonon excitations give raise to complex phenomena, such as high thermal conductivities, that are otherwise unexplained. As another example, collective excitations, at variance with conventional diffusive transport, can induce wave-like heat propagation, or second sound. This had been found only in a few exotic materials at cryogenic temperatures, but is present instead routinely in 2D materials at room temperature. The correlated-phonon description of heat transfer can be rationalised by introducing a new collective excitation, called 'relaxon', which is defined as the eigenstate of the collision operator. Whereas only oversimplifying assumptions endow phonons with well defined relaxation times (the average interval of time between collisions), relaxons have always well defined relaxation times and permit an exact description of thermal transport. The complex dynamic of heat transport in 2D is thus greatly simplified and a kinetic gas theory of thermal transport still applies, provided that the gas is not constituted by phonons, but by relaxons. Our work on thermal transport is part of a larger effort, aiming at the creation of a database of numerically computed properties of materials. The high-throughput production of simulated properties is a challenging task, since it necessitates the understanding of a physical model, but it also needs to face a myriad of technicalities and problems that hinder the execution of a large number of calculations. In order to allow the creation of computational materials databases, we developed AiiDA, an open-source automated interactive infrastructure and database for computational science. This platform tackles the problems of creation, management, analysis and sharing of data and simulations, summarized in the pillars of Automation, Data, Environment and Sharing. Automation is achieved by management of remote computational resources and the encoding of workflows, that allows the execution of complex sequences of calculations. The tight coupling between automation and data storage, handled by the platform, enables full reproducibility of the results and a suitable database design allows for efficient data analysis tools. Sharing of scientific knowledge is addressed by providing tools for distribution of data and of the underlying workflows that generated them, creating an ecosystem for computational materials science.