An oldie but a goodie. IMHO, this paper, along with Larry and Sergei's original work, should be part of every Linear Algebra course. Few things get students to pay attention like the mention of ungodly amounts of money!
The resources already linked from this thread are surely superior but, as a shameless plug, I wrote a blog article recently on this very topic as it was presented in my linear algebra course at CU Boulder: https://thought.place/articles/2017/7/22/pagerank/
I am curious to know what major innovations in search engines happened since the page rank algorithm, or were there only incremental improvements?
Also is search considered a solved problem?
Well...pretty much everything important turns out to be an eigenvector.
Sadly, this seems to be the last thing we've ever heard about the search algorithm of Google. It tells nothing about topics like modern natural language-processing (which defines a different, non-global, ordering of search results, based on the query). How much of the basic algorithm is still in effect?
This article is from 2006. It's interesting but I'd hazard a guess that it's hardly relevant to what Google is doing now.