Recent studies on MgB
2 superconductors are reviewed. MgB
2 single crystals show B
c2 anisotropy factors of 2.6—4.5. The B
c2 of a single crystal at 4.2 K is ∼15 T when the field is parallel to the ab plane. MgB
2 bulks, wires and tapes show a higher B
c2 than single crystals. This B
c2 enhancement can be explained by the introduction of defects that decrease the coherence length. MgB
2 thin films show a much higher B
c2 than bulk materials. The highest B
c2, 49 T at 0 K, was reported for highly resistive MgB
2 thin film. One of the effective pinning centers in MgB
2 seems to be grain boundary. Effective pinning centers are also introduced by nanometer-size impurity additions such as SiC. SiC addition significantly increased J
c values in the high field regions, and hence B
irr. Most tapes and wires are now fabricated by a powder-in-tube (PIT) method. The ex-situ PIT method employs MgB
2-reacted powder and hard sheath materials such as stainless steel. The J
c of ex-situ tapes sensitively depends on the packing density of the MgB
2 core. A maximum J
c of ∼4.5×10
5 A/cm
2 is obtained at 4.2 K and zero fields. Ex-situ processed tapes show J
c anisotropy with respect to the field orientation due to the grain alignment. The in-situ PIT method employs a powder mixture of Mg and B. High-energy ball milling and mechanical alloying of the starting powder mixture enhanced the J
c values. The replacement of MgH
2 with Mg is effective for improving the reactivity and enhancing J
c values. The J
c at 4.2 K and zero magnetic field reached 2—3×10
6 A/cm
2. The highest J
c, 2.5×10
4 A/cm
2, was obtained at 10 T and 4.2 K when SiC was added to in-situ processed tape prepared with MgH
2+B powder. This J
c is comparable to that of a commercial Nb-Ti conductor.
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