Recent studies on MgB2 superconductors are reviewed. MgB2 single crystals show Bc2 anisotropy factors of 2.6—4.5. The Bc2 of a single crystal at 4.2 K is ∼15 T when the field is parallel to the ab plane. MgB2 bulks, wires and tapes show a higher Bc2 than single crystals. This Bc2 enhancement can be explained by the introduction of defects that decrease the coherence length. MgB2 thin films show a much higher Bc2 than bulk materials. The highest Bc2, 49 T at 0 K, was reported for highly resistive MgB2 thin film. One of the effective pinning centers in MgB2 seems to be grain boundary. Effective pinning centers are also introduced by nanometer-size impurity additions such as SiC. SiC addition significantly increased Jc values in the high field regions, and hence Birr. Most tapes and wires are now fabricated by a powder-in-tube (PIT) method. The ex-situ PIT method employs MgB2-reacted powder and hard sheath materials such as stainless steel. The Jc of ex-situ tapes sensitively depends on the packing density of the MgB2 core. A maximum Jc of ∼4.5×105 A/cm2 is obtained at 4.2 K and zero fields. Ex-situ processed tapes show Jc 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 Jc values. The replacement of MgH2 with Mg is effective for improving the reactivity and enhancing Jc values. The Jc at 4.2 K and zero magnetic field reached 2—3×106 A/cm2. The highest Jc, 2.5×104 A/cm2, was obtained at 10 T and 4.2 K when SiC was added to in-situ processed tape prepared with MgH2+B powder. This Jc is comparable to that of a commercial Nb-Ti conductor.