The Internet is probably the most important technological creation of our times. It provides many immensely useful services to the masses for free, including such essentials as web search, web mail, and web portals. These services are expensive to maintain, and depend upon advertisement revenue to remain free. One of the most effective ways to allocate advertisement space on the web is through auctions. In this talk, I will discuss some of the theoretical challenges in the design of online advertisement auctions, and will present some of our recent results addressing these issues. In particular, I will focus on mechanism design for budget-constrained bidders, multi-unit auctions for perishable goods with unknown supply, and dynamics of bid optimization.