A comprehensive review of the first principles phonon calculations is given here with special interests on their applications to metals and ceramics science. Thanks to the progress of high-performance computers, first principles phonon calculations are now practical with the accuracy comparable to experiments. They can be made using an ordinary PC-cluster within a reasonable research timeframe. A variety of thermal properties can be estimated from the phonon states. Firstly, we describe the harmonic approximation and derivation of heat capacity at constant volume, Helmholtz energy and entropy. Then, we explain the quasi-harmonic approximation that treats volume dependence of phonon states. Heat capacity at constant pressure, thermal expansivity and Gibbs energy can be evaluated. Next, we explain a method to compute lattice thermal conductivity by taking account the third order anharmonicity. We show how to trace the collective motion of atoms associated with phase transitions and deformation twins by analyzing imaginary phonon eigenvectors. We also briefly describe challenges of self-consistent phonon calculations to include higher order anharmonicity and electron-phonon interactions. Reliable phonon calculations have become routine because of the development of robust software and their persistent maintenance. Finally, some open-source codes are exemplified.