MPs begin debating the Human Fertilisation and Embryology Bill, an updated version of the current legislation which became law in 1990, this week.
It was drafted because of a feeling the existing law was increasingly out-dated and irrelevant to scientific advances made in the last 20 years.
But several of the key issues are causing bitter divisions of opinion.
Prime Minister Gordon Brown was forced to offer a free vote on three controversial areas in order to avert a rebellion by Catholic MPs.
Here, we set out the debate on those three points, plus a bid to reduce the abortion time limit - also controversial - which is set to be discussed as an amendment to the Bill.
A hybrid embryo is a mixture of animal and human tissue.
Scientists in the UK are already working on one specific type of hybrid.
These are created by transferring DNA from human cells, such as skin cells, into animal eggs that have had virtually all their genetic information removed.
The resulting embryos are more than 99% human, with a small animal component of around 0.1%.
They are then grown in the lab for a few days before being harvested for stem cells, immature cells that can become many types of tissue.
Two licences to create this type of hybrid embryo have already been granted by the Human Fertilisation and Embryology Authority, and a team in Newcastle has successfully produced them.
The Bill would also allow for the creation of other types of hybrid embryos:
No hybrid embryo would be allowed to develop beyond 14 days. It is already illegal to implant human-animal embryos in the womb or bring them to term.
What are the arguments in favour of this process?
Scientists who advocate the work say the cells would allow them to study how genetic defects, which cause diseases such as Parkinson's, develop.
They also say that stem cells' ability to develop into different tissues mean it could be possible to use cells formed in this process to cure diseases.
Using animal eggs would enable scientists to overcome the problem that human eggs are in short supply.
What are the arguments against?
Opponents say it is tampering with nature, and is unethical.
Existing legislation requires IVF clinics to consider the "welfare" of any child created. That currently means considering the need for a father.
The new Bill says this should no longer be the case.
What is the argument in favour?
It is said that some lesbian couples and single women have not been allowed to have treatment, and those in favour of the change - including government ministers - say removing the need for that consideration means that would not occur.
After criticism, the wording in the Bill has changed from considering the need for a father to needing "supportive parenting".
What is the opposition to this proposal?
Opponents say the phrase "supportive parenting" denigrates the role of fathers in a child's life
They say retaining the need to consider the need for a father would reinforce the importance of role, but not prevent single women or lesbians from having treatment.
Tory peer John Patten has said recently that having a father brings a range of practical and spiritual benefits to a child, including better health, education and future earning power and less chance of criminal behaviour.
He said a having a father figure also provides boys with a positive role model to look up to.
Saviour siblings are babies born because they are a tissue match for a sick older brother or sister with a genetic condition.
Cells from the baby's bone marrow or umbilical cord are used to treat the older child.
It is only considered where conventional treatment, such as using an existing family member as a donor, has been ruled out.
Embryos are created using the mother's eggs and the father's sperm. They are then allowed to develop to the eight-cell stage, which takes two to three days.
One or two cells are removed from each embryo, and tested to see if they have the genetic flaw responsible for the existing child's illness.
An embryo which is a tissue match, but unaffected by the gene flaw, is then implanted in the mother's womb for it to develop.
This type of tissue typing has already been permitted for six families, although it is not explicitly covered by the 1990 Act.
Preimplantation genetic diagnosis (PGD), the technique used to see if an embryo is a match, is legally permitted now if a genetic condition is present in a family.
It can be used to check an embryo does not carry any one of 50 different conditions including cystic fibrosis and Duchenne muscular dystrophy.
What is the argument in favour?
That children who have no other hope of treatment for serious medical conditions could be helped, at no detriment to their new brother or sister.
What is the argument against?
There are fears children will be created as saviour siblings alone, and not because they are a wanted child.
There are also concerns that PGD will be used to select male or female embryos, even when there is no risk of a genetic condition. Some sex selection is already permitted, if the condition concerned is something such as Duchenne muscular dystrophy, which primarily affects boys.
The upper time limit for abortions is not addressed in the main Bill, but Conservative MP Nadine Dorries is tabling an amendment which means it will be discussed at the same time.
She, and those who agree with her, want to see the time limit reduced to 20 weeks, from 24.
The argument centres on a foetus's "viability", and around the improvements in the treatment of babies born prematurely, and at what stage they can survive.
What is the argument in favour of reducing the limit?
Ms Dorries says babies born at 24 weeks are increasingly likely to survive, and it should therefore not be permitted to abort pregnancies at this stage.
Right-to-life groups add that efforts should be made to save every life.
And what is the argument against?
Studies, including one published in the British Medical Journal this month, show that while survival rates have increased significantly for babies born at 24 and 25 weeks, they have not risen for babies born 23 weeks or less.
Very few terminations take place at this stage of pregnancy.
But those in favour of keeping the limit as it is say that. since it is the 20 week scan which reveals severe abnormalities, parents need time to make a decision about whether they are going to keep the baby.