Hypercapnia or the increase in arterial carbon dioxide tension (PaCO
2
) above normal values (4–6.5 kPa, 30–48 Torr) is often observed in patients with pulmonary disease, patients with a drug‐induced reduction of the ventilatory drive (for example, because of administration of opioid‐like drugs or anesthetics), or is artificially induced to study the ventilatory control system (for example, by increasing inspired CO
2
to study the effects of drugs on this control system). In this short review, we will focus on the latter, i.e., the mathematical description of the ventilatory controller and some techniques to measure the ventilatory drive. Note that the model(s) we will discuss can be applied to “chemical control of breathing” only. Chemical control of breathing is control dependent on arterial blood gasses (e.g., PaCO
2
, PaO
2
, and pH), and it is active during states of mental relaxation, such as non‐REM sleep, anesthesia, and possibly physical relaxation. The models do not apply to the respiratory effects of exercise or behavioral/emotional activities such as eating, speaking, and playing a musical instrument.