Sorry for the late response. This is a repost of an older answer of mine.

Sometimes you might hear that Soviet "archives" were open in the early 1990s, and then completely closed. I think what I love the most about the idea of the Russian archives being closed is that it makes me think of the scene at the end of Raiders of the Lost Ark. It's all in a big secret vault!

Unfortunately, it's nothing like that. First of all, because there isn't a single "Russian archives". There's a single federal Russian archival agency - Rosarkhiv, but it oversees a number of archives. Fifteen major archives, in fact.

The State Archives of the Russian Federation is the main archive, and includes state documents from pre-Revolutionary times. For Communist Party of the Soviet Union archives, these are mostly in two separate archives: the Russian State Archive of Socio-Political History (RGASPI) has party records mostly prior to 1952, while records since are in the Russian Archive of Contemporary History (RGANI). These latter have a lot of classified material (ostensibly to protect still-living persons).

Of course in addition to these, there are governmental archives not under Rosarkhiv. These include the archive of the President of the Russian Federation, as well as the archives of the Foreign Ministry, Intelligence Services, and the military. These are essentially "working archives", meaning that they are actively in use by governmental agencies, and are hard to get into. Items from the KGB and NKVD (and other iterations of the secret police) were supposed to be declassified and transferred to Rosarkhiv in the early 1990s, but this never happened. In 1991, one could in theory wander into the KGB archives and look at whatever you wanted, but as J. Arch Getty noted in 1996, this was an incredibly brief power vacuum for all the Russian archives, and thereafter, even in the early 1990s, when Rosarkhiv erred on the side of public transparency, it needed to restrict access to at least be in line with standard world archival practices.

Since 2000 archival access for researchers has been decidedly mixed. It can be (like dealing with any Russian governmental agency) an agonizingly slow and uncertain bureaucratic process to gain access to archives, often heavily relying on personal connections. Items that are available can suddenly be classified. Nevertheless, the general trend is towards declassification, notably with items from Stalin's personal archives being declassified and released in the past several years.

The hardest items to access - and increasingly so - tend to be NKVD archives. Again note that they aren't part of Rosarkhiv, and a researcher needs to get permission from the FSB to access them. Last year Russian courts sided with the FSB in barring access to troika panel documents from the Stalin-era purges, while even more worryingly it is destroying records of Gulag inmates once those individuals have reached the age of 80.

So the trend has been towards more difficulty in accessing files, but it is still nowhere near the complete classification and secrecy of the Soviet era. It really depends what you are trying to research and where (remember that Russia is a federation, so there are regional archives as well as central archives - similarly the other former Soviet Socialist Republics have their own archive systems, which range from wide open to slammed shut).

Historians also have to use ingenuity to bypass obstacles in dealing with the various archival systems and levels of classified access. A notable example I can think of is Russian historian Oleg Khlevniuk, a senior researcher at GARF. Although most NKVD archives and documents are classified, he managed to hunt down literal carbon copies of NKVD documents attached to memos and circulars in unclassified party and prosecutorial archives.

So: the various Russian archival agencies all have acted differently: some information is freely available, some is increasingly hard to access, some is actively being declassified, and some was never available to the general public in the first place.