We employ state-of-the-art first-principles calculations based on density-functional theory and densityfunctional perturbation theory to investigate relevant physical properties and phase diagram of the free guest type-I (X-46) and type-II (X-34) carbon clathrates. Their properties and those of silicon and germanium diamonds, and clathrates have been computed and compared within the same approach. We briefly present and discuss their structural, cohesive, and electronic properties. In particular, we present different results about electronic properties of carbon clathrates. From the symmetry analysis of electronic states around the band gap, we deduce their optical properties, and we forecast the effects of hypothetical-doped elements on their electronic band gap. We then report first-principles calculations of vibrational, thermodynamical, and elastic properties. Whereas vibrational properties of Si and Ge systems can be linked through their atomic weight ratio, we show that the vibrational properties of carbon structures differ strongly. Raman and infrared spectra of all clathrates are also calculated and compared. The effects of pressure and temperature on thermodynamical properties ( heat capacity, entropy, thermal expansion, etc. (within static and quasiharmonic approximations are investigated. It is shown that thermodynamical properties of carbon clathrates and diamond present a similar evolution up to high pressures (100 GPa) and over a large range of temperatures 0, 1500 (K). Then we deduce the equilibrium phase diagram (P, T) of C-2/C-34/C-46. We conclude the paper with a presentation of elastic properties computed from acoustic slopes.