Ammonia borane (NH3BH3, AB) has a hydrogen capacity of 19.6 wt-%, exceeding that of gasoline and making itself an attractive candidate for hydrogen storage applications. Great efforts have been paid to research the low cost and highly efficient catalysts for hydrogen generation from the hydrolysis or methanolysis of AB in the past decade. Copper is admitted as being a promising catalyst, being as reactive as noble metals and much more cost effective. In this review, we focus on the research progresses of the Cu based nanocatalysts in dehydrogenation from AB for chemical hydrogen storage.