Your fireplace system, from top to bottom:
The chimney cap keeps objects from falling into the chimney and, with a spark arrester, keeps sparks from escaping.
The chimney flue, made from insulated metal or terracotta, safely carries combustion gases up the chimney.
The smoke dome and wind shelf are designed to work together to funnel smoke and gases out the chimney.
The damper, a door made of cast iron or steel, regulates the draft up the chimney.
The firebox contains the fire and sends smoke upward. It also maximizes heat radiation into the room.
The ash pit is a fireproof storage area for ash. It's accessed through a cleanout, a small metal door outside.
The foundation supports the weight of the fireplace and chimney, distributing it evenly to the ground.