First Chechen War - Russians whom resided there were facing their own little ethnic cleansing thanks to the crazy separatists and all guided by an ex Soviet general aiming for his own little kingdom. Such cleansings mixed in with terrorist attacks elsewhere, adding in an incompetent leader like Yeltsin and a bad economic time, help lead to the disaster of the first war.
Second Chechen War - Chechnya had de-facto independence. They squandered it and attacked Daegestan (or was it Ingushetia?) and thus sparked the second war. Second war was aided with the assistance of foreign agents, especially George Soros groups, and Saudi Arabia/Pakistan whom had sent their own Wahabist fighters into the region. Many of these so called "freedom fighters" by the idiot west were arabs and not even Chechens. As well, they cannot be called Freedom fighters when they attack a republic of Russia that voted to stay part of Russia and did nothing to receive the aggression.
Georgian War - Happened when Medvedev was in power. Georgians got cocky regarding how Tie Eater Shaka was to obtain "western backing" since he obtained all this modernized equipment with the assistance from Israel, and US provided a lot of training (as well as sending Georgians to Afghanistan for boot lickings). The cockyness ended up costing the lives of various Russian Peacekeepers in South Ossetia when Georgia launched an attack using artillery. This sparked Russia to retaliate and well, force the independence of the breakaway republics of Abkhazia and South Ossetia. Whom were both fighting against Georgia since the 90's for independence. This wasnt the first conflict Russia had with Georgia. I think first one was in 93. At that time, there were three breakaway republics.
First and Second Chechen war, Putin wasn't in power yet. Second Chechen war happened in August 1999 and Yeltsin was in power till December 1999. Putin came into power in May 7, 2000 for the first time. That is when also in May 2000 Second Chechen war ended and start the anti insurgency/counter terrorism started. That lasted for 9 years and now after finally dealing with majority of the terrorists there, have moved onto Daegestan and Ingushetia to deal with counter terrorism. Actually, in this case, you can say they been dealing with counter terrorism in these regions for at least over a decade. And well, prior to Soviet Union, for over a hundred years?
Georgian War was different of course, but Putin wasn't responsible for both either. Putin wasn't President in 1993 and wasn't either in 2008 (he was PM). Conspiracy theorists blame him for everything, and so do the nutjobs in the west (politicians and what not). But if you do the dates/times and what not, he isn't at fault for them. He could have had some responsibilities involving them, and he is directly responsible for the counter terrorist operations since, but not the flat out wars themselves.