It caused a bonanza of weapons to flow from the Eastern Bloc to former Soviet client states. They still needed weapons, so arms merchants like Viktor Bout stepped in and filled that gap. Often times with the alleged knowledge of the FSB (the successor to the KGB).

Viktor Bout is the flashiest example of the post Soviet collapse arms trade, and there's a book about him called Merchant of Death: Money, Guns, Planes, and the Man who Makes War Possible that details his activities in the period before his arrest. He moved millions of dollars of weapons all over the world using a fleet of Soviet planes that he "Acquired" during the chaos of privatization...but the biggest market was West Africa where he supplied pretty much every horrible dictator or rebel group around.

If you would like an in depth book on the aftermath of the USSR's collapse and the subsequent shift in arm trading, I would suggest picking up Ken Silverstein's Private Warriors. It is a fabulous work of investigative reporting and covers not just the illegal arms trade but US foreign policy and the increasing retirement of US military figures jumping into the private arms business. Im afraid I don't posses the expertise to speak on this authoritatively, but from what I understand, the work is well regarded and I hope you will like it as much I have.