A microscopic understanding of thermal transport is of broad interest for the design of efficient energy materials, and requires a detailed knowledge of atomic vibrations (phonons) in order to establish reliable microscopic models of thermal conductivity. Neutron and X-ray scattering and optical spectroscopy measurements can map phonon dispersions throughout reciprocal space, providing a quantitative information on the mean-free-paths of heat-carrying vibration modes, and revealing dominant scattering mechanisms, including anharmonicity, electron-phonon coupling, and scattering by defects or nanostructures. Such microscopic information about the microscopic origins of thermal transport provides important insights to design more efficient thermoelectric materials, for example. In addition, first-principles simulations of the atomic dynamics enable the rationalization of extensive experimental datasets. In particular, finite-temperature calculation of the phonon self-energy and spectral functions allow us to capture striking effects of anharmonicity. In this presentation, I will present results from our recent investigations of thermal transport in several important thermoelectric materials [1-3]. Further, phonons often provide a large contribution to the entropy of materials, and I will discuss several cases where our investigations contributed to a detailed understanding of the free-energy and phase-stability, highlighting recent results on thermodynamics of the metal-insulator transition in VO2 [4] and in multiferroic compounds.