Understanding and quantifying the fundamental physical property of coherence of thermal excitations is a long-standing and general problem in physics. The conventional theory, i.e., the phonon gas model, fails to describe coherence and its impact on thermal transport. Recently, we theoretically developed a generalized law for the decay of the phonon number taking into account coherence effects. Before the conventional exponential decay due to phonon-phonon scattering, this law introduces a delay proportional to the square of the coherence time. This additional regime leads to a moderate increase of the relaxation times and to a different dependence of phonon relaxation to those . Then, we proposed a general heat conduction formalism supported by theoretical arguments and direct atomic simulations, which takes into account both the conventional phonon gas model and the wave nature of thermal phonons. Our theory and simulations reveal two distinct types of coherence, i.e., intrinsic and mutual, appearing in two different temperature ranges . The phonon coherence theory also demonstrated that the strong phase correlation between local and non-propagating modes, commonly named diffusons in the terminology of amorphous systems, triggers the conduction of heat. By treating the thermal vibrations as collective excitations, the significant contribution of diffusons, predominantly relying on coherence, further reveals unique temperature and length dependences of thermal conductivity . Our works  establish a fundamental frame for understanding and quantifying the coherence of thermal phonons, which should have a general impact on the estimation of the thermal properties of solids.