The firebox is the area that contains the fire; it is commonly constructed of either metal sheeting or firebrick. Since the heat of the fire keeps the firebox clean, very little upkeep is required.
Gently scrub the walls of the firebox opening with a stiff-bristle brush (not a wire brush) only to the height of the lintel (the heavy steel brace that supports the masonry above the fireplace opening).
Be gentle with firebrick because it crumbles easily. Be careful not to bend any edges on a metal firebox where it joins the flue. Bent edges leave openings to the wall stud or supports where fire could spread.
If your fireplace does not have an ash pit or box, shovel the bulk of the ashes into a bag and vacuum the remaining lightweight ashes.