  Flat bands imply lack of itinerancy due to some constraints that, in
principle, results in anomalous behaviors with randomness. By a molecular
orbital (MO) representation of the flat band systems, random MO models are
introduced where the degeneracy due to the flat bands is preserved even with
randomness. The zero modes of the chiral symmetric system with sublattice
imbalance belong to the class. After explaining the generic flat band
construction by MOs, several examples are discussed with numerical
demonstration as sawtooth lattice in one dimension and hyper-Pyrochlore lattice
in any $d$-dimensions that extends the Kagome ($d=2$) and Pyrochlore ($d=3$)
lattices to general dimensions.
