Last week activists, responding to a call from the Extinction Rebellion group, laid siege to Shell's London headquarters whose windows were smashed.
Several days later hundreds of activists blocked several symbolic sites in France, including the headquarters of oil giant Total.
"They are mastodons whose business model is based on fossil fuels and which don't want to shift one iota because up until now they've made money that way," said Cecile Marchand, who heads up climate activities of the French branch of the Friends of the Earth network of environmental protection groups.
"The activities of these multinationals are not at all regulated today, and they should be if we are to be serious about the idea of limiting global warming to 1.5 degrees" Celsius, she added, referring to the goal laid out in the 2015 Paris climate deal.
The pressure isn't only coming from environmental activists.
"Investment funds are now requiring oil and gas companies to explain how climate change might affect a company's value," said David Elmes, a professor at Warwick Business School.
"This is driving some companies to be much more transparent about the emissions they cause and their plans to reduce them," he added.
The big actors in the sector -- BP, Chevron, ExxonMobil, Saudi Aramco, Shell, Total and others -- have banded together in the Oil and Gas Climate Initiative (OGCI), which has a billion-dollar war chest to fund initiatives to reduce climate change emissions.
The companies are trying to limit their methane emissions, which escape when fossil fuels are taken out of the ground and transported.
Along with agriculture, the energy industry remains a key source of methane, which causes more warming than carbon dioxide.
Other energy giants are trying to counterbalance their carbon footprint, like the Italian group ENI, which has promised to plant vast forests.
CEO Claudio Descalzi has said "our objective is to achieve net zero emissions in our upstream business by 2030" via emission reductions and offsets.
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The industry has also taken on board a strategic shift towards using more natural gas -- which has a lighter carbon footprint than oil -- as well as producing electricity via renewables like wind and solar.
Shell recently surprised observers by declaring its ambition to become the world's top electricity producer by 2030.
But some environmental groups point to the fact that energy companies are still pouring most of their investments into pumping out more fossil fuels.
"These companies want to continue exploiting fossil fuels as long as possible," said Marchand. "For them, climate change doesn't matter."
While the spectacular plunge in oil prices in 2014 led to a drastic cut in investment in exploration and development by energy firms, such spending is on the rise again.
Plans by oil and gas majors to spend $4.9 trillion on fuel exploration are incompatible with the goal of the Paris climate deal to limit the rise in global temperature rises, according to an analysis released earlier this week by the pressure group Global Witness.
"The evidence that people are looking for is whether companies are shifting the billions they invest each year away from fossil fuels," said Elmes at Warwick Business School.
"While some companies are making commitments to do so ... the percentage being invested in non-fossil fuel businesses are still small."
To achieve the Paris targets, oil consumption needs to begin declining dramatically in the next couple of years, according to estimates by the International Energy Agency, which would only be possible by a major shift by the transportation sector towards electric vehicles.
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