I thought that it was about time that I took a look at Yandex which says of itself "We are the leading internet company in Russia, operating the most popular search engine and the most visited website. We generated 60.2% of all search traffic in Russia in April 2012, and our Yandex sites attracted 46 million unique visitors in March 2012. We also operate in Ukraine, Kazakhstan, Belarus and Turkey. Our mission is to answer any question internet users may have." Basically that means that while we use Google, Russian and similar countries use Yandex.
It's a fairly basic search engine, since it only searches Web, Images and Video. It has a mail client as well, but I can't imagine that you're all tripping over each other to use it, so I'll ignore that. Results are arranged by relevance, but it does have an option to search on date instead, which is something that a lot of searchers are particularly keen on.
The results page is fairly sparse - title of the result, a short summary, full URL and a cached version. However, it does attempt a combination approach by also including images and video results if appropriate. Finally, searchers can also search within a set of results as well, with a simple tick box toggle. There is an advanced search option which highlights the use of - to exclude terms (although confusingly on my screen they use the ~ symbol instead), and the ability to search within a specific website (but you can't broaden that to include country or other domains such as .gov.uk). Searchers can limit to where words appear (anywhere, title, exact, or in any grammatical form, which I take to mean in any order), in one of 8 languages - mainly Russian and similar, when a page was last updated (with an additional option to add in your own custom date), and in particular formats, such as .pdf, .doc and so on. Yandex didn't get the concept of OR and NOT and so it's very limited in that respect, and certainly no competitor to Google - or indeed most other second league search engines that you're familiar with.
Image search is very similar to that offered by Google - size, orientation, type, colour, file, date and from specific sites. Video search is fairly basic - thumbnail of the video (drawn from a variety of different sites), title, summary and URL.
Yandex was interesting to wander through, but ultimately very unsatisfying. The one thing that I did like was the ability to quickly re-rank by date, but it was otherwise very unremarkable. Not one that you'll be adding to your search engine armoury any time soon I suspect.