Unlike a localized state induced by defect in a crystalline solid, the so-called flat band is truly a Bloch state but yet without band dispersion. It arises from destructive interference of Bloch wave functions, independent of the single-particle crystalline Hamiltonian (i.e., the strength of lattice hopping). Flat band can host a range of exotic quantum phases, such as ferromagnetism, Wigner crystallization, superconductivity and high-temperature fractional quantum Hall effect. In this talk, I will first briefly review lattice models which give rise to 2D/3D flat bands including a new Coloring-Triangle lattice we found recently. I will then discuss real flat-band materials including our recent work on pyrochlore Sn2Nb2O7 which hosts 3D flat bands. A novel mechanism for the formation of Weyl points enabled by doping of doubly degenerated 3D flat bands, instead of symmetry breaking of a Dirac point, will also be discussed.