Russian military forces have largely withdrawn from Georgia, but have fortified in South Ossetia and Abkhazia, regions which have sought autonomy and independence. At the same time, Russia is preparing to recognize the regions' independence, according to the New York Times. As it retreated, Russia destroyed Georgian armories and military installations.
Georgia has become a darling of the West and has been moving towards becoming a member of NATO, the US's European military alliance. It has already received substantial military assistance from the U.S. With its invasion of Georgia, which Russia claims was justified to protect South Ossetia after Georgia sent military forces to seize the capital of Tskhinvali on August 7, Russia has sent a clear message to the U.S. that it not only disapproves of encroachment into its own sphere of influence, but is prepared to take military action to defend its own perceived self-interests.
Georgia provides a key oil pipeline route providing the West energy from the otherwise Russian-dominated Caspian Sea region. Russia's willingness to use force to keep small regions in its sphere of influence is mostly a symbolic gesture. Russia has made no secret that it would like to see Mikheil Saakashvili, Georgia's pro-U.S. president, ousted, and if that were somehow a result of the political turmoil the crisis has caused Russia would no doubt be pleased (according to Ambassador Kurt Volker, the U.S. has warned Saakashvili not to use military force to try to deal with the South Ossetia issue). But such an outcome seems unlikely, and the most Russia really seems to have accomplished is in sending the message to Washington that if it pushes, Russia is willing to push back a little bit.
Russia may have miscalculated, however. Immediately following the invasion of Russian forces into Georgia, the U.S. and Poland promptly sealed a deal to provide Poland with a missile defense system. Washington has ludicrously claimed the system is to defend Poland from Iran, but Russia, naturally, has clearly not been convinced by this argument that the purpose is not to further contain Russia and limit its influence. Of course, the U.S. can't possibly expect Russia to believe this line, but then neither does Washington feel it prudent to come out publicly and explicitly state the purpose for the missile defense deal (the purpose, that is, besides monetary profit).
Russia has taken its own jabs at the U.S. In attempting to justify its invasion, Russia claimed that Georgia had engaged in "ethnic cleansing" in South Ossetia, an apparent means by which to compare Russia's actions in Georgia with the NATO bombing of Kosovo, which served only to escalate real atrocities that were taking place on the ground.