The collapse of the big European empires, concluding with the disintegration of the Soviet Union, left the US as the only superpower, leaving it as something of a global "empire." The quotes are appropriate because in recent decades the US has not attempted to permanently occupy or politically incorporate foreign nations. Of course this hasn't kept us from interfering in the rest of the world, sometimes militarily.
The old empires of Europe mostly seem content with their fate, except of course for Russia, which under Putin has annexed a few former colonies and continues to hint and push for more ambitious goals. These annexations have been the old-fashioned kind, by military force, though so far confined to former colonies with substantial pro-imperial sentiment.
Meanwhile, the Chinese empire has forcefully reasserted itself, propelled by a surging economy and renewed self-confidence. So far, the main targets of its imperial advances have been Tibet, Hong Kong, and Taiwan, but they are also making threatening noises in the South China sea.
Since all these new contenders, and some more minor powers, are packing nukes, this resurgent empire building presents a fundamental challenge to the Pax Americana, and a real threat to the age of rapid economic growth that much of the world has seen in recent years. Past experience with aggressively growing empires is not promising.
I'm not sure what to make of the contrasts. China seems to be expanding mostly because of its reborn economic strength - Russia because of its continuing economic weakness.