More than 100 abortions every year are carried out late - after the 24-week point in a pregnancy.
Abnormalities can be detected by ultrasound
They happen because doctors have detected a "physical or mental abnormalities " in the foetus which would cause it to be born "seriously handicapped".
A Church of England curate is challenging a decision to go ahead with a late abortion in the case of a foetus with cleft lip and palate.
The courts are being asked to decide whether a further police investigation is needed.
What does the law say about "late abortions"?
The time limit on abortions is governed by the Human Fertilisation and Embryology Act of 1990.
Some types of abortion have a time limit of 24 weeks.
These are where doctors believe there is "risk of injury to the physical or mental health" of the pregnant woman - or one of her existing children.
However, some abortions have no time limit, and can be legally be carried out right up until the baby is due to be delivered.
This covers terminations where there is a risk to the life of the mother if the pregnancy continues, or a risk of "grave permanent injury" to her mental or physical health.
In addition, abortion is allowed without time limit if there is a "substantial risk that if the child were born it would suffer from such physical or mental abnormalities as to be seriously handicapped."
All abortions must be agreed by the mother and two doctors.
How often does it happen?
Figures suggest that last year, there were 110 abortions carried out post 24 weeks in England and Wales.
In total, 185,000 abortions were carried out in England and Wales in 2002.
Who decides whether the abnormality is serious enough?
At the moment, doctors decide in consultation with the woman involved.
The wording of the Act is deliberately vague, deferring to the clinical of judgement of doctors rather than setting standards elsewhere.
However, some doctors are uncomfortable about the burden this places them under.
There have been some suggestions that "qualifying" conditions should be listed, or that abortion should not be allowed in the last third of pregnancy unless doctors can definitively diagnose a condition that will lead to a very early death.
This would disqualify abortion on the grounds of Down's syndrome or spina bifida in the final three months of pregnancy.
On the other hand, many doctors argue that deciding that one condition is "serious" and another "trivial" on the basis of their own beliefs can be wrong.
The mother may place far more importance on a specific type of abnormality than perhaps the consulting doctors would.
Why 24 weeks?
The 24-week limit broadly represents the point at which a foetus becomes potentially viable.
However, technological advances mean that babies born this early do have some chance of survival, and some born even earlier have survived.
What actually happens in a late abortion?
Even if the pregancy is to be terminated, the foetus, which may well be growing at the normal rate, still has to be delivered along with the placenta.
Beyond the 24 week mark, many foetuses, even those with severe abnormalities, would be born alive after an induced labour.
Often, the foetus is part-delivered before a medical procedure to terminate it is carried out.
How common are abortions on the grounds of conditions such as cleft lip and palate?
The available statistics do not precisely identify the number of foetuses aborted because of cleft palate after 24 weeks.
In 2001, there were four terminations citing "severe abnormality" involving cleft lip and palate.
However, some experts say that cleft lip and palate may be a marker for a multitude of severe congenital abnormalities.