Internet ad auctions are a fascinating innovation with a huge impact. From both a system and an algorithmic/economic point of view, advertising systems involve the interplay of many components. I will give an overview of this interaction and describe some problems and theoretical results in this domain. This will include some well-known results on budget allocation, as well as new problems and results in the increasingly important domain of auto-bidding. Time permitting, we will discuss some new questions at the intersection of machine learning and mechanism design.