For green activists such as Friends of the Earth, ExxonMobil is "the number one global warming villain". Its former chairman and chief executive, Lee Raymond, who retired at the end of 2005, was dubbed the "Darth Vader of global warming" and an "enemy of the planet" by environmental campaigners.
The environmental lobby targeted the oil major not so much for what it has done but for what it has said. Although its contribution to greenhouse gas emissions is greater than those of competitors such as Royal Dutch Shell or BP, it is in the same order of magnitude
But Exxon's executives, and groups it has supported financially, have been vocal in their scepticism about the evidence on climate change and among the most outspoken critics of the Kyoto protocol, the international climate change treaty.
Fresh allegations surfaced this week over the role of Philip Cooney, now an Exxon employee, in softening scientific reports on climate change when he was an official in the Bush administration.
But under Rex Tillerson, Mr Raymond's successor, Exxon is trying to overturn those perceptions. It recognises that no company can afford to exclude itself from the mainstream of the debate on climate change - least of all the world's biggest energy business.
"We feel like we need to get out and be heard ourselves, rather than let other people - including the press - define who they think we are," says Sherri Stuewer, Exxon's vice-president for safety, health and the environment. "For quite some time we have said that we recognise that the accumulation of greenhouse gases in the atmosphere poses risks, and that those risks could prove significant, not only for people but for ecosystems. And on the basis of that risk we are certainly taking actions in our own operations to create the [emissions] reductions.
"I think that position has not been well understood. And perhaps we have not done a good enough job of getting it out."
Exxon denies that the attacks on it by environmental campaigners have forced a change of stance. The protests and boycotts do not seem to have had a noticeable impact on its bottom line. But for a company as scientifically based as Exxon - it has 2,000 science and engineering PhDs on its staff - becoming isolated from the mainstream of scientific thought put it in an uncomfortable position.
Refusing to respond to the threat of global warming has increasingly looked like a poor strategic decision. As the evidence has hardened, previously sceptical voices have been changing their tune or falling silent. Tomorrow the biggest report to date on the state of climate science, from the Intergovernmental Panel on Climate Change, will say with 90 per cent certainty that climate change is happening and is likely to result in a 3°Celsius temperature rise by 2100.
John Llewellyn, senior economic adviser at Lehman Brothers, says: "Companies that see climate change coming, recognise it for what it is, do the relevant R&D and inculcate a positive attitude to change on the part of their management stand to do very well. A company that doesn't believe it and doesn't encourage its managers to take it seriously is going to get rolled over."
Exxon is not making a great strategic U-turn or trying to position itself "beyond petroleum", as did BP. It is unapologetic about its conviction that fossil fuels will continue to dominate the world's energy supplies, and hence its own business, for the next two decades at least.
Mr Raymond notoriously cut R&D into renewable energy on the grounds that none of the alternatives to oil and gas could be commercially viable. Exxon still has no investments in wind, solar, or nuclear energy. But it is highlighting its joint ventures with Toyota and Caterpillar researching ways to improve fuel and engine systems.
It has joined the European Union's CO2 Remove project, looking at ways to capture and store carbon dioxide emissions from power stations. It has promised $100m (£51m, €77m) over 10 years to Stanford University's Global Climate and Energy Project, conducting early-stage research into potential future energy sources.
It has also moved a long way in its engagement with the debate over the right response to global warming. Many of the fiercest attacks on Exxon came over its support for think-tanks and lobby groups that challenged the scientific consensus on global warming, such as the Competitive Enterprise Institute.
Last month the Union of Concerned Scientists, an environmental campaign group, published a report arguing that "to serve its corporate interests, ExxonMobil has built a vast echo chamber of seemingly independent groups with the express purpose of spreading disinformation about global warming".
Ms Stuewer rejects the charge that Exxon has supported "junk science" on climate change, saying its arguments have been over policy responses, not the scientific evidence. "Often organisations have been characterised as sceptical on the issue of climate when their comments have really been focused on Kyoto as a policy," she says. "We need to be clear that questioning whether Kyoto is the right approach to climatepolicy is not and should not be synonymous with being a climate sceptic."
Exxon has long supported serious climate science, she says, at institutions such as the Massachusetts Institute of Technology, Columbia, and Britain's Hadley Centre.
But it has recently dropped its funding for several groups, including the CEI, and taken up support for others, including Resources for the Future, a non-partisan think-tank.
But despite this shift, Exxon still categorises climate change as a "century-scale problem" issue and advises that policy responses "start gradually and learn along the way".
That runs counter to the view of the urgency of global warming taken by the scientists of the Intergovernmental Panel on Climate Change, the body convened by the United Nations to advise on global warming. Its report, drawing on the work of 2,500 climate scientists over the past six years, will warn that climate changes are already taking place and will accelerate. As a result, Rajendra Pachauri, IPPC chairman, has advised cutting emissions quickly and substantially.
Charlie Kronick, senior policy adviser at Greenpeace, says: "If [Exxon] is taking this position [that there is time to gradually decrease emissions over several decades] they can't be serious. The science tells us very clearly the problem is urgent.
"This isn't a long-term problem," he says. "Scientists are telling us we have 10 to 20 years to take action against climate change."
Exxon has also not yet formed a view about which policies it would advocate. As it admits, its support risks putting the kiss of death on any proposal.
Inside the company, policy options are being debated, and Exxon has set out principles that should guide policy. These say, among others, that it should promote global participation, maximise the use of markets to promote efficiency and be as transparent as possible for both businesses and consumers.
But Ms Stuewer gives a pointer towards what Exxon might eventually support. "I think we've been fairly consistent in our position that target-setting, as embodied in the Kyoto protocol, had some pretty serious flaws. Among them is that it does not seem to be an effective way to bring the developing world into participating in greenhouse gas emission reductions," she says.
"Cap-setting is extremely difficult, both practically and politically. Mistakes in that process can end up producing volatility - and that volatility makes investment planning very difficult."
Ed Crooks and Fiona Harvey