Structural and superconducting properties of MgB₂ are strongly anisotropic. Therefore investigations of its intrinsic properties should be performed on single crystals rather than on polycrystalline samples with randomly oriented grains. Unfortunately, conventional methods of crystal growth did not work for MgB₂. High temperature solution growth in metals (Mg, Al, Cu, etc.) at normal pressure used for other borides is not possible due to very low solubility of MgB₂ in these metals or formation of other compounds. The solubility of MgB₂ in Mg is extremely low up to the boiling temperature of Mg (1107 °C) at ambient pressure. At higher temperature solubility increases, but partial pressure of Mg vapor above molten Mg increases with temperature, at temperature of crystal growth (1800-2200 °C) is very high and using of high pressure methods is necessary. Single crystals of MgB₂ have been grown from flux with a high-pressure cubic anvil technique. Investigations of the P–T phase diagram prove that the MgB₂ phase is stable up to 2200 ^oC at high hydrostatic pressure. Superconducting and normal state properties of pure MgB₂ are now well evidenced by experiments and explained by theory. However, modification of properties through chemical substitutions is still not well understood. Specific band structure of MgB₂ with two bands, π and σ, involved in superconductivity is strongly influenced by chemical substitutions. Substitutions of Al for Mg and C for B dope MgB₂ with electrons and lead to increase of scattering within both π and σ bands, however, with different rates for both elements. Therefore, different changes of the upper critical field, H_c2, and its anisotropy, gamma_Hc2, for Mg_1-xAl_xB₂ and MgB_2-xC_x are observed. By introduction of C, Al, Li, Mn, Fe in the melt we were able to substitute partially Mg or B in MgB₂ crystals and to dope the crystals with electrons or holes. Hole doping with Li decreases superconducting transition temperature, T_c, but in much slower rate, than electron doping with C and Al. In the crystals co-doped simultaneously with both Li and C or Li and Al one can expect compensation of electron doping with C or Al by holes from Li and increase of T_c. In this presentation the review of the results of crystal growth of pure and substituted MgB₂ crystals as well as investigations of the structure and superconducting properties is given.

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