Expansion
Only a few decades ago it was widely assumed that the universe was rather stable - that it was in a "steady state". This view was held largely because there wasn't enough information to suggest otherwise. A competing view, the Big Bang, was an idea that had existed alongside steady state for decades but was not accepted until the cosmic background radiation was found that showed the universe had a beginning from a single point. This meant that the universe had been expanding from it's initial explosion.
Acceleration
The relatively recent discovery in the nineties that the expansion of the universe is expanding rather than holding steady or decreasing has had a similarly shocking effect. Current theory holds that after the initial explosion, the expansion of the universe was decelerating due to gravity until about 5 billion years ago. At that time, the rough distribution of matter was spread apart enough for the expansion to begin accelerating.
New Theories
Acceleration has spurred physicist to rethink the nature, structure, and material of the universe. Based on what we know about the visible matter, the universe should be slowing it's expansion, not accelerating. As a result, cosmologists have started a search for exotic or dark matter (dark' because we can't see it) to explain the acceleration. It is possible that none of the current theories of exotic matter will pan out, and there may be some other explanation entirely. However, dark matter, whatever it may turn out to be, is currently leading the pack.
Cosmologists have even begun to think about what may have happened before the Big Bang. It is now thought that our universe may simply be one of many, like bubbles in soap foam. There may be parallel universes lurking very near ours with slightly different laws of physics, or there may be "many worlds" of universes that are related to our own, having branched off at common points in the past.
Cosmology in the post Big Bang era has proven to be one of the most fertile area of physics, and will likely be one of the most active areas of physics well into the coming centuries.
