Synchrotron radiation photoemission spectroscopy and low energy electron diffraction (LEED) are applied to explore several novel materials: (a) Ce epitaxial growth on W (110) surfaces; (b) Eu epitaxial growth on Ta (110) surfaces; (c) Sm epitaxial growth on Ta (110) surfaces; (d) quasicrystalline AlPdMn; (e) superconducting Ba[subscript]1-xK[subscript] xBiO[subscript]3. In the case of rare earth overlayers on transition metal surface, resonance photoemission spectroscopy is used to enhance the 4f features. The metal surface phase transition is investigated on an atomic-scale. In the case of quasicrystalline AlPdMn and superconducting Ba[subscript]1-xK[subscript] xBiO[subscript]3 the electronic structures are investigated by angle-resolved photoemission;We have grown thin Ce films epitaxially on W(110) up to multiple layers. In the first monolayer, a continuous [gamma]-[alpha]-like phase transition is observed. The epitaxial orientation is the Nishiyama-Wassermann type. Above one monolayer the film transforms to normal [gamma] phase Ce with a 30 degree rotational phase transition. The thick film is unusually oriented with Ce (011) parallel to the substrate (110) (Homma-Yang-Schuller orientation);Photoemission and LEED studies of Eu(110) surfaces have successfully determined that the Eu(110) surface exhibits an fcc-bcc-like phase transition. The Eu(110) surface top layer is reconstructed to hexagonal-close-packed plane. This surface phase transition might be similar to the bulk martensitic phase transitions of bcc metals;Combining both photoemission and LEED observations we find a Sm surface divalent-to-trivalent phase transition occurred on the Ta(110) substrate. At submonolayer coverage the surface is divalent with no ordered overlayer structure. The single monolayer Sm overlayer transfers from divalent to trivalent and the structure is ordered hexagonal. The lattice is expanded 6% relative to the ideal close-packed Sm(0001) surface. The second monolayer is divalent and this top layer is reconstructed. The reconstruction of the surface top layer results a 5 x 5 LEED pattern;The angular-resolved energy distributions for photoelectrons emitted from the fivefold surface of single crystal icosahedral AlPdMn are presented. A quasi-periodic upward dispersion of 300 meV of a spectral feature at 2.3 eV binding energy is observed with 13 eV photon energy. A distinct pseudo gap feature is observed with a density of states near the Fermi level that decreases as a power Law; LEED studies confirm the existence of quasicrystalline order at the surface;The electronic structure of Ba[subscript]0.6K[subscript]0.4BiO[subscript]3 is investigated by angle-resolved photoemission on a single crystal (001) surface. The results show metallic character with a featureless low density of states within 1.5 eV of the Fermi level. Most of the DOS is located between 1.5 and 5.5 eV binding energy below E[subscript] F. Three flat bandlike features in between about 2.6 eV and 5.0 eV are observed. A fourth weak feature around 6.6 eV is also identified. Compared with the LAPW band structure calculation, there is a rigid downward shift of the complete band structure by an energy of order 1 eV and K doping might introduce disorder features.