Games have benchmarked AI methods since the inception of the field, with classic board games such as Chess and Go recently leaving room for video games with related yet different sets of challenges. The set of AI problems associated with video games has in recent decades expanded from simply playing games to win, to playing games in particular styles, generating game content, modeling players etc. Different games pose very different challenges for AI systems, and several different AI challenges can typically be posed by the same game. In this article we analyze the popular collectible card game Hearthstone (Blizzard 2014) and describe a varied set of interesting AI challenges posed by this game. Collectible card games are relatively understudied in the AI community, despite their popularity and the interesting challenges they pose. Analyzing a single game in-depth in the manner we do here allows us to see the entire field of AI and Games through the lens of a single game, discovering a few new variations on existing research topics.