Metal borohydrides have been studied since the beginning of this century as potential hydrogen storage materials due to their high gravimetric hydrogen content. Many new compounds have been synthesized and characterized, however to date the main problem are the kinetics of dehydrogenation and rehydrogenation. In this review we address thermodynamical and chemical properties of boron hydrogen compounds which come into play for hydrogen storage and which must be considered in the search for efficient catalysts. More recently, closo and nido hydridoborate and related closo hydridocarborate compounds have been identified as good ionic conductors for all-solid-state lithium or sodium batteries. The properties of these fascinating and very promising compounds for battery applications are illustrated with recent literature results.