So, in the United States, of course, there is the 10th Amendment to the constitution, stating that powers not enumerated as adhering to the federal government are reserved either to the states or to the people. In practice, this means there are several powers (education, welfare, and transportation come to mind) that really are the province of sovereign states. Even if federal laws supercede state ones in many instances, states still have the right to appeal to the Supreme Court if their sovereignty has been impugned.
In the days of the USSR, individual republics had, I am at least led to believe, a similiar level of authority. Boris Yeltsin, for example, rose to prominence precisely because he was able to secure Russia's rights over against the disintegrating USSR.
The question then is about the current Russian Federation. To what extent are the constituent members sovereign entities? For example - could Chechnya or other autonomous Oblasts nullify a federal power? Is there an entity to which the regions can appeal a federal power? Or, are the constituent regions more akin to the Dillion Rule which states that counties are mere administrative divisions of the state?
In other words, what does federalism look like in the Russian Federation?