Hypersonic vehicles seems all the rage these days - China reportedly tested one, named Wu-14 on August 7, the United States made an attempt to test its own on August 25. Neither of these tests was a success, but it is clear that the tests will continue. What about Russia?
Russia first went public with its "hypersonic weapon" more than ten years ago - in February 2004 it tested a warhead that according to the Kremlin "will fly at hyper-sonic speed and will be able to change trajectory both in terms of altitude and direction, and missile defence systems will be powerless against them".
The warhead in question appears to go all the way back to the 1980s. One of the projects developed by the Chelomey Design Bureau (NPOmash) after 1987, an Albatross (solid-propellant) ICBM, included some kind of a maneuverable warhead. In 1989 the Albatross missile system was transferred to other design bureaus (and became Universal, which then became Topol-M), but NPOmash apparently kept the warhead. It was tested at least twice - on 28 February 1990 and 5 March 1990. Katayev's notes are a bit cryptic on these tests, but he noted that both tests were conducted "without separation" and mentions "70-80 km altitude." The vehicles flew to Kamchatka. Additional flight tests, including ones "with separation," were planned, but it looks like the first two flights were the last ones for some time.
The tests were resumed in the 2000s. We know that the strategic exercise on 18 February 2004 included a test of a UR-100NUTTH missile that flew from Baykonur to Kamchatka. This was later identified as a test of the new "hypersonic vehicle". It might not be the same Albatross that was flown in 1990, but it's probably related. As it turns out, there must have been a test in 2001, probably in June, although it went unannounced at the time. More reports of new tests appeared in 2011 - a new warhead was tested on a UR-100NUTTH missile on 27 December 2011 and I was told that it was related to the "hypersonic" project. The program was apparently alive and well.
More details appeared about a year ago, thanks to Alexander Stukalin, who found a number of interesting documents that mention Project 4202 and construction activity at the Object 370 at the Dombarovskiy missile base. At that point it was not quite clear what Project 4202 is and whether it is related to Object 370. Everything pointed to a new payload that will be carried by a UR-100NUTTH/SS-19 missile, even though the evidence was somewhat circumstantial. But now we have some new documents (you've guessed who found them) that link together quite a few elements of the project.
A working document of the Central Design Bureau of Transport Machine-Building (TsKBTM) describes "fueling of the A35-71 [missile] with propellant components during tests at the Object 370 conducted as part of the work on Project 4202." This is a fairly direct evidence of the link between Project 4202 and Object 370. Also, the document refers to a contract signed in March 2009 - apparently Project 4202 was formally started around that time.
Unfortunately, the exact location of Object 370 remains somewhat elusive. We know that it's at Dombarovskiy, but the satellite imagery there is rather old - there is nothing after 2009. There are a few good Panoramio photos from May 2013 that show some serious construction at an old command center (51°3'42"N 59°36'30"E) and at some other silos, but these are a bit farther from Yasnyy than Object 370 (which is about 7 km from the city).
At the same time, the silo at 51.093482° 59.844589°, which is adjacent to a command center, seems to be a good candidate for Object 370.
There is one more link between Project 4202 and the UR-100NUTTH missile - in June 2014 the KBKhA Design Bureau placed an order to explore the extension of service life of rocket engines used in the UR-100NUTTH missile to 42 years. The assignment explicitly said that the extension is done as part of another project - extension of service life of the 15S300-4202 system. Since 15S300 is the designation for the 15A35/UR-100NUTTH/SS-19 missile without the payload section, it's reasonable to assume that 15S300-4202 is that missile adapted for Project 4202. As we can see from this order, the missiles that will be used in the new system are rather old - I don't think any UR-100NUTTH were produced after 1984 - but the engines have been kept dry all these years, so they must have aged gracefully.
The payload, which apparently includes that "space head section" (the suspected "hypersonic" vehicle) is designated 15Yu71 (15Ю71, see the discussion and links in comments). It looks like that production of the 15Yu71 (or at least some of its key components) will begin in 2015. By that time the infrastructure at the Dombarovskiy site should be fully ready.
Indeed, it's quite possible that the Dombarovskiy site was used for a flight test of the new system already - there was a report about an unsuccessful test of a "hypersonic vehicle" that took place in September 2013. The report was contested, but I think I have fairly strong evidence that there was indeed a test. Whether the missile was launched from Dombarovskiy is rather difficult to say, but I would not rule it out.
So, the bottom line is that Russia is fully in the "hypersonic race", although we may have to wait a year or two before we see the fruits of the Project 4202.