"Hello, world!" by Bump of Chicken is the opening theme (Single released circa April 22, 2015) for Japanese anime series "Kekkai Sensen" AKA "Blood Blockade Battlefront", while "Sugar Song to Bitter Step" by UNISON SQUARE GARDEN closes the show. The MV below is the "Short Version" of the song, released May 20th.
Shown here are the "original" music videos, while I will attempt to post the anime sequences on my iNot Otaku!-blog :)
I have been gleefully following the anime for the past 9 episodes (as of this post) and thoroughly enjoyed the music used - from the OP and ED songs posted above, to the big band / swing music within the show itself (Check a preview of the OST), and to me personally, is one aspect of which makes this is anime as successful and evocative.