So, how do they get better at it? According to research just published by Roffey Park Management Institute, one the things that managements can do is to play down the traditional view of leadership.
"Creative people tend to be self-motivated; they are unlikely to look for innovative solutions if they are led by someone who slavishly follows the corporate line," said John Whatmore, who has headed the two-year project.
Successful creative team leaders, the researchers add, are also likely to be experts with strategic knowledge of the field; able to choose team members with complementary differences; able to help team members know each other quickly; supporters of others; developers of the creative skills and talents of team members; and "empathetic, warm and approachable".
On the other hand, the study at the West Sussex management centre, backed by the Department of Trade and Industry's Innovation Unit and several organisations with an interest in managing creativity, identified eight ways of stifling creativity. These included keeping too tight a rein on creative teams; letting go of the reins completely; abandoning support for personal development; appointing accountants, lawyers and administrators, rather than experts in the area concerned, to head teams; keeping people separated from one another through divide-and-rule policies; and only rewarding prima donnas.
Mr Whatmore looked at a range of activities - from scientific research at organisations such as the Wellcome Foundation, through BBC Radio to Olympic athletics coaches - in his analysis of the work of 38 project group leaders. "Our findings indicate that creative groups are different; and they require different skills to manage them successfully," he said. He added that organisations can limit creativity by being either too bureaucratic or too market-oriented.
"Organisations can be awkward settings for creative output. Too heavy an emphasis on success can discourage risk-taking. Companies that do not encourage personal development tend to be the very antithesis of those in which creativity flourishes."
Mr Whatmore, who has extensive experience of a variety of businesses, said the study came at a time when creativity and the leadership of creative groups are of ever greater importance in organisations of all kinds, while abilities in this area were still limited.
Another apparent paradox was that success seemed to depend on fostering both "chaos and its opposite". Doing that was a great art since it meant having what one person involved in the study called "freedom and control at the same time".
Consequently, the skills and talents of people who manage or lead creative groups appear to be distinctly different from those required in other types of group. They are more to do with the general development of individuals and their talents and with creating or sustaining culture and atmosphere than with achieving specific objectives.
Moreover, although creative people are often regarded as difficult to manage, there are some managers, according to Mr Whatmore, who have a gift for getting the best out of them.
The aims of the study were to discover at the level of first line supervisor (because that is the biggest and most influential area) what makes one person more effective than another, the ways in which different projects call for different characteristics, and the factors that have contributed to the development of effectiveness in managers and leaders.
The idea is that greater understanding might help in the development of the processes of selection and training of managers in other organisations where innovation is becoming increasingly important.
As a result, Mr Whatmore and his colleagues are planning seminars with participants to pursue the issues thrown up by the study.
"We're going to experiment with ways of helping people to get better at it," he said.