The pons - the name means bridge and in part the pons is a bridge to the higher brain. However its main functions are as part of the regulation of the rate and depth of respiration. It also contains the CNS connection for cranial nerves V, VI, VII, and VIII.
The medulla - center for the vital functions of heart rate, respiration, and blood pressure. The medulla also has CNS connections for VIII, as well as IX, X, XI, and XII. The pyramids are also part of the medulla. The medulla stimulates the muscles of respiration and controls the breathing rhythm. It regulates the heart rate and volume and controls blood pressure and overall blood distribution.