We review the discovery of new phases of carbon (Q-carbon) and BN (Q-BN) and address critical issues related to direct conversion of carbon into diamond and hBN into cBN at ambient temperatures and pressures in air without any need for catalyst and the presence of hydrogen. The Q-carbon and Q-BN are formed as a result of quenching from super undercooled state by using high-power nanosecond laser pulses. We discuss the equilibrium phase diagram (P vs T) of carbon, and show that by rapid quenching, kinetics can shift thermodynamic graphite/diamond/liquid carbon triple point from 5000 K/12 GPa to super undercooled carbon at atmospheric pressure in air. Similarly, the hBN-cBN-Liquid triple point is shifted from 3500 K/9.5 GPa to as low as 2800 K and atmospheric pressure. It is shown that nanosecond laser heating of amorphous carbon and nanocrystalline BN on sapphire, glass, and polymer substrates can be confined to melt in a super undercooled state. By quenching this super undercooled state, we have created a new state of carbon (Q-carbon) and BN (Q-BN) from which nanocrystals, microcrystals, nanoneedles, microneedles, and thin films are formed depending upon the nucleation and growth times allowed and the presence of growth template. The large-area epitaxial diamond and cBN films are formed, when appropriate planar matching or lattice matching template is provided for growth from super undercooled liquid. The Q-phases have unique atomic structure and bonding characteristics as determined by high-resolution SEM and backscatter diffraction, HRTEM, STEM-Z, EELS, and Raman spectroscopy, and exhibit new and improved mechanical hardness, electrical conductivity, and chemical and physical properties, including room-temperature ferromagnetism and enhanced field emission. The Q-carbon exhibits robust bulk ferromagnetism with estimated Curie temperature of about 500 K and saturation magnetization value of 20 emu g−1. We have also deposited diamond on cBN by using a novel pulsed laser evaporation of carbon and obtained cBN/diamond composites, where cBN acts as template for diamond growth. Both diamond and cBN grown from super undercooled liquid can be alloyed with both p- and n-type dopants. This process allows carbon to diamond and hBN to cBN conversions and formation of useful nanostructures and microstructures at ambient temperatures in air at atmospheric pressure on practical and heat-sensitive substrates in a controlled way without need for any catalysts and hydrogen to stabilize sp3 bonding for diamond and cBN phases.