Non-functioning ovary, endoscope view. The ovary (centre, white) and its Fallopian tube (pink). An ovary releases the eggs (ova, female reproductive cells) that travel through the nearby Fallopian tube to the uterus (not seen). This is the right- hand ovary of the two in a woman's abdomen. There are many possible causes of infertility in women, but in some cases the cause is unknown.