Here's a breakdown of the respiratory system pathway:

1. Trachea: The windpipe, carries air from the throat to the lungs.

2. Bronchi: The trachea splits into two main bronchi, one for each lung.

3. Bronchioles: The bronchi further divide into smaller and smaller tubes called bronchioles.

4. Alveoli: At the very end of the bronchioles, the tiny air sacs called alveoli are found. These are the sites of gas exchange between the air and the bloodstream.

So, the bronchioles are the final branching structures before the alveoli.