What challenges exist for Russia in the 21st century?
Russia has a number of obstacles and challenges in the way of it becoming a stable and prosperous country, but they have also come a very long way in the last 20 years since the 1991 revolution.
Their economy has stabilized, and even in the midst of world recession, Russia's balance sheet is really quite strong. Exports have risen and government revenues are way above where they were. The military is no longer an empty shell and pensions and medical care are more widely sustainable than they were a few years ago. Russian industry has turned a few corners from the days when they were a socialist state, and is more competitive on the world market.
That being said, the new Russia face some old challenges. They have a very active mafia that holds sway in soe parts of the country (though much less so than a decade ago). Russia's vast resources are still, for the most part, untapped. There is a national problem with alcoholism that dates back to the Soviet era, and there has been little effort towards democratic reforms. Vladimir Putin, though officially out of office, still wields most of the power in government through intermediaries. There is still a rather large disparity of wealth between Russia's new economic elite and the average citizen, and they have a declining birthrate.