I have just watched a news video of a Soyuz rocket taking off from Baikonur and noticed that there is no trail of smoke like you see on the American launchers. It left the sky quite clear. Why is this?

It burns kerosene, which doesn't leave much of a smoke trail. American rockets (like the Space Shuttle) have solid rocket boosters which leave quite a smoke trail. If you look carefully, you'll notice the liquid-fueled engines on the Space Shuttle (the center ones) leave no trail -- they burn liquid hydrogen.

Thanks, I guessed it must be something like that. So the next question is what are the advantages and disadvantages of the two systems?

From what I understand solid-fueled boosters can provide more power but are uncontrollable: once you light them up they just go. Liquid-fueled boosters have the advantage of being fully throttlable, and some can even be turned on and off multiple times throughout the flight.

It burns kerosene, which doesn't leave much of a smoke trail. American rockets (like the Space Shuttle) have solid rocket boosters which leave quite a smoke trail. If you look carefully, you'll notice the liquid-fueled engines on the Space Shuttle (the center ones) leave no trail -- they burn liquid hydrogen.

Not to mention most of the "smoke" in the beginning is really steam.

Not to mention most of the "smoke" in the beginning is really steam.

 

You can't see steam either. What you see is small water droplets that have condensed from steam.