This talk will go over the basics of the PageRank problem, studied initially by the founders of Google, which allowed them to create their search engine by applying it to the internet graph with hyperlinks defining edges. Then, I will explain our new results on the problem for undirected graphs, whose main application is finding local clusters in networks, and is used in many branches of science. We have now algorithms that find local clusters fast in a time that does not depend on the whole graph but on the local cluster itself, which is significantly smaller. This is joint work with Elias Wirth and Sebastian Pokutta.