... but speculation about its classified missions hasn't yet come to earth.
Given the lack of evidence that the X-37B sidled up to other satellites, the most likely missions have been testing the spacecraft's performance and hauling intelligence-gathering equipment into low orbit.
But what kind of equipment? There it gets interesting. Let's think beyond remote-sensing that's pointed at obvious targets like aircraft carriers, defense factories, seaports, air bases, and mobile-missile testing facilities. Nor is it likely that it's been spying on other satellites (or the Chinese space station) with a telescope, given the enormous closing speeds.
How about satellite-stealth-related experiments? This is a subject I track given my features on unmanned spacecraft and stealth tactics. I can think of three stealthy subjects the X could assist with.
Snooping on other countries' stealth aircraft: If the X's payload bay carried the latest technology in infrared (IR) sensing, it might be peering down on flights of China's new stealth aircraft, the J-20, to check for heat signatures. Such an infrared telescope would be mounted inside the X's payload bay, and brought back to earth for upgrading at the end of each trip.
What about stuff moved outside the bay, temporarily or otherwise?
The X could be helping in tests of the latest satellite-stealth measures. Perhaps the USAF is shoving a small, low-observable (“stealthy”) experimental satellite out of the X's bay, and then keeping the X nearby, to facilitate ground-based sensing. That would allow the test satellite to get into low orbit without detection, since there'd be no separate classified launch for nosy people to watch.
Since the X could stay close enough to keep tabs on the testbed satellite's exact location, that would help in analyzing how well distant USAF sensors (on ground or in space) can do in spotting the elusive satellite.
Background: The USAF considers satellite-stealth something we'll need in case of conflict. But keeping a satellite off a first-tier enemy's monitor screens won't be easy. For example, radar stealthiness (which requires materials to absorb radar energy) tends to raise the spacecraft's surface temperature whenever it's in sunlight. The waste heat makes it more detectable by infrared telescopes.
To explain: radar stealth argues for a dull, black, absorptive coating on the satellite (as I saw on the B-2A's exterior surfaces when visiting Whiteman AFB for articles) but infrared stealth argues for a mirror-like surface to reflect sunlight, ideally away from the Earth. There is some talk of nano-tech to solve this dilemma. That may be possible, but it would need a lot of testing.
Another possible stealth approach that the X could help test is simply to reduce the test satellite's radar signature to something that looks like space junk, at least on radar. There's a lot of junk to hide among (image, Wiki Commons):
That's a cheaper form of stealth than nanotechnology. If a tactical satellite could hide among the debris cloud, the USAF wouldn't have to worry as much about infrared emissions, since all the other debris is giving off IR as well. That approach is rather likely in the near term, in my mind.
Less likely mission, but interesting: the X could be helping to test a prototype gravity gradiometer (GG). This is probably not ready for prime time; maybe in a few years. The GG is said to have the potential to spot enemy satellites that are otherwise completely stealthy in terms of radar, infrared, and visible light. If such enemy satellites weigh a few hundred kilograms or more, a network of GG satellites might detect them dozens of miles away. This would require a networked web of detector satellites, each taking and reporting its own measurements to the X by radio.