tec: First there was the big bang. Our laws break down the closer you get to the big bang meaning we not only dont know anything about the before, but also the emediately after (10^(-40) seconds after or something like that). There are also other things that are mysterious, for example inflation and so on.
TODAY there are plenty of stuff we dont know about the universe. For example how quantum mechanics and gravity connects, or what dark matter is. This is not a trivial thing: Dark matter(energy) constitute about 95% of the universe, but we dont know what it is at all.
That is why there is such an exitement about the big accelerator in CERN: we may verify that our current world-view makes sence (NOT a final theory of anything!), or it may be blown to bits. There may also be given hints on what dark matter/energy is, and what stuff such as 'time' is. the 21st century may be as exiting as the 20th!
The future looks very grim: We can observe that the universe is expanding, that has been known for about 50 years. Quite recently we have observed that not only is everything moving apart, the expansion is accelerating. It seem that 'vacuum' is pushing the universe apart. If this continue, everything will be torn apart in some billion years, there wont even be atoms, just ever-expanding space. That will be the end of everything.
There are plenty of ideas regarding the conditions around big bang, but nothing concrete yet. With respect to the big bang, we are stone age men wondering what the moon is.