The experimental realization of atomic Bose-Einstein condensation at ultracold temperature has led to rapid advances in creating and manipulating cold molecules, and which has given birth to a new research field of quantum matter-wave superchemistry. Contrary to the classical Arrhenius law, the tunnelingdominated ultracold reactions can be realized through the highly-controlled magneto-optical technique. Novel quantum effects have been identified in these cold reactions, such as the super-selectivity rule in dissociating triatomic molecules, and the quantum size （vessel-shape） effect. In this review, we focus on a variety of new achievements in this fascinating matter-wave wonderland, including the quantum finitenumber effect and double-slit interference in assembling cold molecules, the quantum noise in triggering collective abstraction reaction, and the magnetic phase transition in a laser-catalyzed quantum spin-mixing gas. The practical applications of matter-wave superchemistry are also introduced, such as the optical information storage via quantum photo-association, and the laser-enhanced creation of spinor or even chiral molecules.
