The first-generation search engines struggled to meet users' needs. Search engines had a tough job to do. The Web was growing at an exponential rate. Often thousands of webpages contained information on the query terms. And spammers were purposely trying to deceive the search engines. Fortunately, in 1998, two algorithms came to the rescue. These two algorithms, PageRank, which is used by Google, and HITS, which is used by Teoma, exploited the enormous directed graph created by the hyperlink structure of the Web to rank the thousands of relevant pages by their importance. These rankings dramatically improved search, so that nearly every engine today uses some link analysis algorithm. In this survey talk, I'll present the PageRank and HITS algorithms, emphasizing the fundamental mathematical and computational issues involved. Undergraduate students in mathematics and computer science, especially those interested in linear algebra and numerical methods, should find the talk very accessible.