Yes, they work, but you are going to pay for it.
I have a cheap-ass 15$, 99% @ 1 micron HEPA filter and I noticed the difference, but it by no means elminited all the dust.. I'd say it cut it down by a good 40% though.
They're rated by their efficiency at a certain micron rating, and by the ammount of air they can filter. Ultra Cheap ones are 99% @ 3 or 1 microns and only good for a small room.
Better...99.9% or 99.95% at 1 but usually 0.3 microns.
Best.. 99.99% at 0.3 microns(Commands a hefty premium).
And then you get into the UHEPA.. Ultra High Efficiency Particulate Air (filters).
99.99% at 0.1 microns or less... Think hospitals, and a much, much thinner wallet.
And then you have to think about filters. You have to weigh the cost of the filter, and the ammount it's going to need to be changed.
Cheap HEPA units are 3-6 months.. Better ones are 1-2 years. The key is a good, washable prefilter. There is no point in clogging your expensive filter up with huge 30 micron particles when a cheap foam filter will do it.
Expect to pay at least 100$ for a quality unit.
Do not even think about garbage like the Ionic Breeze.