Orbital is a degree of freedom independent of charge and spin, which is characterized by orbital degeneracy and spatial anisotropy. It plays important roles in magnetism and superconductivity in transition metal oxides. Recently, cold atom optical lattices have provided a new opportunity to investigate orbital physics. In this talk, we will present many novel features in such systems that do not appear in transition metal oxides as follows. Bosons, as recently demonstrated in experiments, can be pumped into high orbital bands and stay with a long life time. We will show that such meta-stable states of bosons exhibit a class of novel superfluid states with complex-valued wavefunctions spontaneously breaking time reversal symmetry, thus are beyond Feynman's celebrated argument of the positive-definitiveness of many-body ground state wavefunctions of bosons. For fermions, we will focus on the p_x,y orbital system of the honeycomb lattice, which exhibits fundamentally different behavior from that in the p_z system of graphene. The interesting physics here includes the flat band structure, the consequential non-perturbative strong correlation effects (e.g. Wigner crystal and ferromagnetism), the frustration in orbital exchange, and the orbital analogy of the quantum anomalous Hall effect.