In order to grown epitaxial magnesium diboride MgB2 films, fibers and heterostructures, an hybrid physical-chemical vapour deposition (HPCVD) technique was developed, which combines physical vapour deposition (PVD) with chemical vapour deposition (CVD). The superconducting and normal-state properties of the MgB2 films are determined by the film thickness. Above 3000Å, a Tc of 41.8 K, a ρ0 of 0.28 μΩ·cm, and a residual resistance ratio RRR of over 30 were obtained. A carbon-containing metal-organic precursor was added to the carrier gas to achieve carbon doping. As the amount of carbon in the film increases, the resistivity increases, Tc decreases, and the upper critical field increases dramatically as compared to clean films. The selffield Jc in the carbon doped film is lower than that in the clean film, but Jc remains relatively high to much higher magnetic fields, indicating stronger pinning. The carbon doping approach can be used to produce MgB2 materials for high magnetic-field applications. We report on structural and superconducting properties of round MgB2 coated-conductor fibers on SiC fibers. The coating is polycrystalline and composed of elongated crystallites. The pure MgB2 fiber shows a zero resistance Tc of 39.3K. The carbon-alloyed fibers show a high upper critical field of 55T at 1.5K and a high irreversibility field of 40T at 1.5 K. The result demonstrates great potential of MgB2 coated conductors for superconducting magnets. We also report structural and transport proprieties of MgB2/MgO and MgB2/AlN multilayers. The epitaxial MgB2/MgO/MgB2 trilayers were grown in-situ in the HPCVD system, while MgB2/AlN/MgB2 trilayers were deposited using an ex-situ process. The results are promising for all-MgB2 planar Josephson junctions.