We discuss the important aspects of synthesis and crystal growth of MgB 2 under high pressure (P) and temperature (T) in the Mg-B-N system, including the optimization of P-T conditions for reproducible crystal growth, the role of liquid phases in this process, the temperature dependence of crystal size and the effect of growing instabilities on single-crystal morphology. Extensive experiments have been carried out on single crystals with slightly different lattice constants and defect concentrations, which have revealed the possible effects of Mg deficiency and lattice strain on the superconducting properties of MgB 2 (T c , J c , residual resistivity ratio, anisotropy, etc).

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