You may have seen these very expensive bags that you place several pillows in or a duvet, then you attach your vacuum to the bag and suck all the air out. The problem with these bags is they have very mixed results. Some work great. Others just leak. I bought some they cost me a fortune and the air kept leaking out.

Well I saw the exact same thing done with a black trash/bin bag. You can use it on anything like pillows, blankets, duvets. Place them in the black bag and gather the open end up around the pipe on your vacuum cleaner. Suck all the air out and you will see that the mass of the item has decreased by about 90%. Simply wrap a rubber band around the end. When you undo the band the items will return to their original size.
However the effectiveness of using trash bags also depends on the make up of the bag, So results have also been mixed using this method.

I have had reports that Zip Lock Freezer bags are very effective and do not leak.

So with a bit of trial and error you should be saving space very soon.

It has also been suggested to uses this suction method when packing to travel. However the problem is when you come home. If you do not have access to a vacuum you will not be able to repack your luggage. Be warned!