Manned space flight, probes to the planets, the hauntingly beautiful images returned by the Hubble Space Telescope - all have been astonishing breakthroughs.
But the biggest advance this century has come in the way we perceive our place in the Universe.
At the close of the 19th century, astronomers thought they had the Universe pretty well stitched up. Newton's gravity ruled absolutely; all celestial bodies obeyed it, moving through space as predictably and precisely as clockwork.
The Universe comprised all the stars in the sky, plus several million others that could be seen through large telescopes.
True, there were mysterious fuzzy patches, which provoked some astronomers to suspect that there could be star systems outside our own - other galaxies - but nobody could prove it.
All that was to change. In the early years of the 20th century two American astronomers - Henrietta Leavitt and Harlow Shapley - laid the foundations of the science of ascribing distances to these "fuzzy patches" by picking out celestial beacons in them: stars called Cepheids, which brightened and faded extremely regularly.
Their work inspired Edwin Hubble to use the then biggest telescope in the world - the Mount Wilson reflector, with its 100-inch-diameter mirror - to make the crucial measurements.
By 1926, no one was in any doubt that these patches were galaxies outside our own, and that the Universe was hugely bigger than anyone had previously thought.
Hubble's work threw up another unexpected first. As well as measuring the distances to the galaxies, he was also able to gauge their speeds. The further away the galaxy, the more quickly it was moving. There was one inescapable conclusion: the Universe was expanding.
This had been predicted 10 years before, in the equations of a formerly obscure patent clerk from Switzerland. Albert Einstein's General Theory of Relativity was a completely new theory of gravity, which described how massive objects deform space itself.
The equations insisted that the Universe must be either contracting or expanding - but, at the time, there was no evidence for such large-scale motion. Einstein, like mathematics students everywhere, therefore put in a "fudge factor" to balance the books. After Hubble's discovery, he referred to this as his "greatest blunder".
The discovery of the expanding Universe was followed by another breakthrough - one that appeared at the time to have little significance.
In 1931, Karl Jansky - a radio engineer at America's Bell Laboratories - was conducting investigations into sources of telephone interference. He suspected thunderstorms, and built a huge antenna aimed at the sky in order to track them down. But what he found instead was static from specific places in the sky - primarily from along the band of the Milky Way.
The implications of his findings were largely ignored by the professional astronomical community. It was down to an amateur, Grote Reber (who is still alive and living in Tasmania), to develop the brand-new field of radio astronomy - which finally came of age after instrumental developments during the Second World War.
It was the first of the "new astronomies", which revealed that merely logging light from celestial bodies gives you but a tiny part of the picture.
Karl Jansky's discovery led to today's multi-wavelength astronomy, with astronomers now able to capture all the radiation emitted by an object - from short-wavelength gamma- and X-radiation to infrared and radio waves at the other end of the spectrum. Each wavelength zone tells you something different about the physics that are going on, allowing today's astrophysicists to take a star to pieces.
It was radio astronomy that led to another giant leap in our 20th-century understanding of the Universe. In 1965, Arno Penzias and Robert Wilson were using a horn-shaped antenna in New Jersey (coincidentally, at the same location where Jansky discovered cosmic radio waves) to detect radiation from the area around our Galaxy. Instead, they picked up a very weak signal from all over the sky - which they first put down to coming from the pigeon droppings coating the inside of their antenna!
But the origin of the signal was more fundamental. The physicist Robert Dicke at nearby Princeton University realised immediately what the researchers had discovered: the afterglow of creation itself.
Now all the pieces were in place. The Universe was expanding because of a vast explosion - the Big Bang. The Big Bang was unimaginably dense and hot - and we still feel a relic of that heat today, in the radiation that was picked up by Penzias and Wilson.
In recent years, astronomers and particle physicists have worked together on the detailed architecture of the Big Bang, and how it led to the Universe in which we live today. They are now even pretty unanimous as to when it all happened: 12 billion years ago.
But the cosmos always has surprises up its sleeve. During the filming of our current Channel 4 series Universe, the American astronomer Bob Kirshner was making routine measurements on the rate of the expansion of the Universe when he was brought up rather sharply. He discovered that the Universe is not just expanding - it is also accelerating.
Where all this will lead, is anyone's guess. It will certainly tax the brains of the scientists of the 21st century. But Kirshner thinks the 20th-century scientists deserve a pat on the back.
"Some people would say this puts human beings in a very minor part of the Universe when you get this big picture," he says. But he goes on: "Even though we have very small brains and live very brief lives, we have been able to build up a coherent picture of how the Universe works. I think we should be proud of that."
THE PLANET Mars - which sets at 8pm this month, and is low on the western horizon - is the world all hopes are pinned on at the moment.
The Mars Polar Lander probe is scheduled to land at the South Pole of the Red Planet on 3 December. Nasa scientists - having lost its predecessor, the Mars Climate Orbiter, to an unfortunate numerical error - have their fingers crossed for its success.
The two main planets lighting up December nights are Jupiter and Saturn (to Jupiter's left).
Both planets are high in the sky mid-evening, and are quite unmistakable. If you have a small telescope, take a squint at Saturn - the rings are presented to us at a nicely open angle at the moment.
Early-morning skies are still dominated by the brilliant planet Venus, which rises three-and-a-half hours before the Sun.
If you are up early at the beginning of December, take a look for its companion inner world, the planet Mercury. The closest planet to the Sun, it emerges from the glare of our local star to rise at 6am for the first week of the month.
Finally, look out for the Geminid meteors, around 14 December. The Moon won't be getting in the way this year, and from a really dark location you may be able to see up to 100 meteors an hour.
7 10.32pm, New Moon
14 Maximum of Geminid meteors
16 12.50am, Moon at first quarter
22 7.44am, Winter Solstice; 5.32pm, Full Moon
29 2.05pm, Moon at last quarterReuse content