We discuss the important aspects of synthesis and crystal growth of MgB2 under high pressure (P) and temperature (T) in Mg-B-N system, including the optimisation 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 crystals morphology. Extensive experiments have been carried out on single crystals with slightly different lattice constants and defects concentration, which revealed and possible effects of Mg-deficiency and lattice strain on the superconducting properties of MgB2 (Tc, Jc, residual resistivity ratio, anisotropy etc.).
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