The Nuffield Council on Bioethics has launched a consultation exercise to find out how the public views current research into anti-social behaviour, obesity, homosexuality, aggression and intelligence.
The scientists involved are also keen to explain their work - and its implications - more fully to the public.
Research into behavioural genetics is controversial not only because of concerns about its scientific validity, but also because of the ethical, legal, social and practical implications it has.
Concerns have already been expressed that this sort of research could lead to discrimination and stigma.
And some groups have expressed fears that identifying the gene responsible for certain behavioural traits might even result in society indulging in eugenics.
Screen babies
Even the Nuffield Council on Bioethics admits that information, once in the public arena, could be put to controversial use.
For instance, it is possible that individuals found to have a gene that predisposed them to criminal activity might be ordered to undergo corrective treatment.
Similarly, babies might be screened while still in the womb to weed out undesirable personality characteristics.
"This is an important area of research that affects the way in which we think about ourselves, and has implications for the way we treat other people.
"Research in behavioural genetics aims to discover genetic influences not only on abnormal or extreme forms of behaviour, but also on normal aspects of our personalities.
"Much of the research is looking at genetic factors that influence traits we all share, though to different degrees, such as anxiety, aggression, and intelligence.
"For this reason, the research has widespread implications for the way we view ourselves, and the way we view other people.
"For example, it has been suggested that if genetic factors are associated with behavioural traits, such as sexual orientation, this may contribute to discrimination and stigmatisation."
Behavioural traits
Last November, the Nuffield Council on Bioethics set up a working party to examine the issues.
It admits there is a big difference between collating genetic information about illness and disease and getting genetic information about behavioural traits.
In its public document, it raises the spectre that if there are genetic breakthroughs, the research could then be misused and manipulated.
The document says: "The central precept of eugenics is the idea that the physical, mental and behavioural qualities of the human race can be improved by selective breeding.
"This means encouraging people who have 'desirable traits' to have children and discouraging, or preventing, those who do not.
"This belief was at least partially responsible for the appalling events of the 20th century in Nazi Germany, and the compulsory sterilisation programmes for mentally handicapped people in North America and Northern Europe."
Dangers and pitfalls
The report says that memories of these human rights abuses still cast a shadow over today's research - particularly in the area of behavioural genetics where there is a chance of social prejudice and racism.
A spokeswoman for Stonewall, the gay rights group, said they welcomed the public scrutiny saying it was important people should be alerted to the dangers and pitfalls of this sort of research.
She said the research had been abused before and that it was important it was not abused again.
"It is interesting that people have used that sort of research to shape their own kind of positions. It is very problematic.
"But it is interesting that there is attention being drawn to the way that these implications can be used and that the public is going to be given a view."