Paid placements on search engines reached sales of nearly $11 billion in the United States last year and represent the most rapidly growing form of online advertising today. In its classic form, a search engine sets up an auction for each search word in which competing websites bid for their sponsored links to be displayed next to the search results. We model this advertising market, focusing on two of its key characteristics: (1) the interaction between the list of search results and the list of sponsored links on the search page and (2) the inherent differences in attractiveness between sites. We find that both of these special aspects of search advertising have a significant effect on sites' bidding behavior and the equilibrium prices of sponsored links. Often, sites that are not among the most popular ones obtain the sponsored links, especially if the marginal return of sites on clicks is quickly decreasing and if consumers do not trust sponsored links. In three extensions, we also explore (1) heterogeneous valuations across bidding sites, (2) the endogenous choice of the number of sponsored links that the search engine sells, and (3) a dynamic model where websites' bidding behavior is a function of their previous positions on the sponsored list. Our results shed light on the seemingly random order of sites on search engines' list of sponsored links and their variation over time. They also provide normative insights for both buyers and sellers of search advertising.