As a fetus grows inside the uterus, some of its physiological processes are very different from our own. After all, this is an individual who is growing inside a muscle sack filled with fluid. If we were suddenly placed into the same muscle sack we would very quickly die because we do not have the necessary means to survive in such an environment. Fetuses however, do. And there are still remnants of our previously way of existing present in our bodies now.

Because fetuses do not breathe air like you or I, they must get their oxygen from the mother. This is obtained via the umbilical vein (remember, just because it is a vein, it doesn’t mean that it carries deoxygenated blood. Vein only means that blood is travelling to the heart, artery means away from the heart) which comes from the placenta. In fetal circulation, blood is not oxygenated via the lungs but via the placenta, so most of it bypasses the lungs by avoiding travelling through the pulmonary artery. This is achieved because there is a hole in the heart between the atria (the foramen ovale) for the blood to pass through. To give you a better idea I will describe the route of the fetal circulation:

Oxygenated blood from placenta enters right atrium via umbilical vein, ductus venosus, inferior vena cava.
This blood mostly bypasses the pulmonary circulation (the blood travelling to and through the lungs), passing through foramen ovale into the left atrium, left ventricle, aorta.
Head and neck receive well-oxygenated blood from first branches of aorta.
Deoxygenated blood passes from superior vena cava into right ventricle, through pulmonary trunk.
Most of this blood bypasses the pulmonary circulation via ductus arteriosus into descending aorta.
Deoxygenated blood leaves embryo via common iliac arteries, internal iliac arteries, umbilical arteries – to placenta.

When the baby is born however, this circulation needs to be changed almost immediately. This is what happens:
Lungs fill with air, pulmonary circulation increases (when the baby cries).
Venous return to left atrium increases.
Flow in umbilical vessels ceases.
Pressure increases in left atrium and closes foramen ovale (which just becomes a small depression in the atrium wall). Also, there is reduced pressure in the right atrium because there is no more blood from the umbilical vein after the umbilical cord is cut.
Ductus arteriosus closes (in response to increases in oxygen tension).
Ductus venosus closes.
Pulmonic and systemic circulations are thus separated.

Remains of this circulation can be seen by:
The oval fossa in the wall of the right atrium.
Ductus arteriosus becomes Ligamentum Arteriosum, which is now just a ligament between the aorta and pulmonary trunk.
On the anterior side of the liver is a ligament called the Falciform ligament made from peritoneum which separates the right and left lobes. Inside this ligament is the remains of the umbilical vein (ductus venosus), called Teres ligament, which bypassed the liver and entered the inferior vena cava.