Abstract: Ultracold atomic gases in optical lattices allow for a wide range of studies at the boundary between atomic and condensed-matter physics. In my talk I will discuss three very distinct experiments that involve lattice-induced diffraction of atomic matter waves derived from a Bose-Einstein condensate. In the first experiment, using a state-dependent lattice potential, we demonstrated a novel type of atomic four-wave mixing in a binary atomic mixture. In the second experiment, using a pulsed incommensurate lattice, we realized a system of coupled kicked quantum rotors in which we observed a quantum-to-classical transition. In the third experiment, we showed that Bragg diffraction of atoms can be used to probe artificial atomic crystals, in analogy to neutron diffraction from conventional solids.