cyclones work via 3 mechanisms 1) gravity pulls particles down. If a particle is small enough to float around in a room then a cyclone can't separate it and a filter is required. Some mdf dust is like this 2) air velocity creates drag on the particle and moves it along the ducting, when it comes into the cyclone it hits the cone wall and slows down, gravity pulls these particles down and they go the bucket 3) They can also reenter the air vortex but at a lower level. The air velocity is slower at the bottom of the cone then the top of the cone, they hit the wall again (due to the circular acceleration pushing them outward) and slow down again. At some point the drag is less then the gravity force and the particle falls out of the vortex into the bucket.
There are horizontal cyclones as well to save space, but verticals are more common...