Gas exchange or respiration takes place at a respiratory surface; a boundary between the external environment and the interior of the body.
For unicellular organisms the respiratory surface is simply the cell membrane, but for large organisms it usually is carried out in respiratory systems.
This name can cause problems; in biology the word "respiration" can mean cellular respiration or metabolism (ATP generation inside cells), however sometimes (such as here) it can also refer to breathing (which is how the word is most often used by non-biologists).
In humans and other mammals, respiratory gas exchange or ventilation is carried out by mechanisms of the lungs.
The actual exchange of gases occurs in the alveoli.