The external iliac artery becomes known as the femoral artery after it passes the inguinal ligament. For a while at this location, (the femoral triangle), it can be known as the common femoral, because it has not yet branched.
It usually gives off a branch known as the profunda femoris or the deep artery of the thigh, while continuing down the thigh medial to the femur. (The profunda femoris is even closer to the femur, and is more posterior).
The femoral artery goes through the adductor hiatus (a hole in the tendon of adductor magnus), into the posterior of the knee. Passing between the condyles of the femur, it becomes the popliteal artery of the popliteal fossa.