For about the past year, things in Chechnya, Dagestan and Tatarstan have been, more or less quiet, though recently there have been a couple of bombings.
The for the most part, you should take caution if you are considering going there. First off, foreigners are easy to spot there and so it would make them big targets for extremists. Secondly, those areas are highly restricted and very difficult to get to if you are a foreigner. The Russian government keeps close tabs on everyone going to that region and can pretty much dictate who can and can not go there. If you do not have official business in going there, you will not be allowed to travel by train or by air.
Thirdly, there is a large presence of Russian military that is specifically designed to keep order and peace there. If a suicide bomber had the chance of taking out Russian soldiers or a foreigner, they would gladly do so in that region. Also, that region has been ravaged by so much war that it would make visiting a very unpleasant experience. When dignitaries go there, they never stay for very long, a quick trip from the airport to whatever function they are attending and then quickly back to the airport to be taken home.
Also, if you take a look at the past 10 years of terrorists attacks in Russia, all of the attacks have been bombings and there are increasing suicide bombers.