There are combustion air ducts, which bring fresh air in for the combustion process. They are generally fairly clean since the are only handling fresh air from outside; maybe fairly dusty if you live in a dusty environment. They should have a ¼” mesh or window screen mesh at the bldg. entrance to keep bugs, etc. out. They should terminate near the heating units, in the Mech. Rm., in a vert. run down to be near the floor, or right into the heating unit, with an open end. Terminating them down into a five gal. bucket, 2/3rds the depth of the bucket tends to reduce the cold air movement into the bldg. unless the furnace is running.
There are exhaust ducts and chimneys which take the combustion products out of the bldg., usually without any mech. power assist, just properly sized and heat rising to exit the bldg. If the water heater and the furnace are gas fired, the flues should be fairly clean, if the burners are properly adjusted. Fuel oil is a little less clean burning, and coal and wood produce the most flue residue. Wood can cause creosote, which clings to the chimney liner and can cause chimney fires. You can see all this stuff, and the need for cleaning, if you look down the chimney with a flash light.
They make round (ball or cylindrical) wire brushes for cleaning the flues. A rope (or rod) on each end, and you just pull them back-n-forth as you progress through the flue. Or, tie the brush to the rope at the bottom of the chimney and pull it up and drop it down in the chimney. It is really messy work, and you would like some forced air from a window fan (or several fans), or some such, blowing into the house (pressurizing the house) so this air exhausts out of the house through the flues you are working on. It is best if you can take the flues apart at the elbows, cleaning them by hand, and otherwise be working on straight runs of duck work. There shouldn’t be a filter in the exhaust flues. It might get plugged and cause carbon monoxide problems in the bldg. There might (by code) need to be a spark arresting screen (and squirrel stop) on the top of the chimney.