Since 1986, a great upsurge in research on activated low-pressure diamond growth from the vapor phase has unfolded throughout the world. The gas sources for low-pressure diamond growth were also extended from C-H binary systems into C-H-O ternary systems. Bachmann’s famous empirical phase diagram (1991) can be explained and improved by our quantitatively calculated projective nonequilibrium phase diagrams, while Marinelli’s critical empirical phase diagram (1994) was near to quantitative agreement with our cross-section nonequilibrium phase diagram on the basis of thermodynamic coupling model. Moreover, theoretical C-H-X ternary nonequilibrium phase diagrams (X = F or Cl) are also in agreementwith experiments reported in the literature. Due to the similarities between allotropic pairs of diamond-graphite and cubic boron nitride-hexagonal boron nitride (cBN-hBN), the new kind of nonequilibrium phase diagrams can also be used for activated CVD cBN processes. Some nice evaluations of nonequilibrium phase diagrams can also be found in the literature.