In brick ovens, 1/4th of the heat leaves through the chimney. A chimney also improves the airflow through the oven. It also helps direct the smoke so it doesn't blow out on your face. An enamelled flue pipe can be used for the chimney. The height of the chimney depends on the size of the oven but it can be anywhere from 1 meter or more. Some people choose not build a chimney in their ovens but that may result in an oven the does not perform at its optimum and may result in excess smoke issues.
The vent of an oven can be constructed with brick, cast, or steel. Each material has its own advantage depending on the usage. The vent of a pizza oven is usually on its outside, not inside. You can use decorative material to hide the vent from the outside. The vent lets some heat escape the inner chamber/dome. There are two places where vents are placed:
In traditional ovens, the vent is in the front, while in central designs the vent is in the centre of the dome and connects to the chimney to let the heat out. The center vent has the benefit of moving the hot air over the top of the oven and may help improve even heat disbursement. There is another design called "vent in the oven" where the vent is placed inside the oven behind rather than in front of the door.