  Orbital degree of freedom plays a fundamental role in understanding the
unconventional properties in solid state materials. Experimental progress in
quantum atomic gases has demonstrated that high orbitals in optical lattices
can be used to construct quantum emulators of exotic models beyond natural
crystals, where novel many-body states such as complex Bose-Einstein
condensation and topological semimetals emerge. A brief introduction of orbital
degree of freedom in optical lattices is given and a summary of exotic orbital
models and resulting many-body phases is provided. Experimental consequences of
the novel phases are also discussed.
