The world’s largest oil companies are girding for the biggest shift in energy consumption since the Industrial Revolution: After decades of growth, global demand for oil is poised to peak and fall in the coming years.

New technologies that improve fuel efficiency are starting to push down the amount of gasoline and diesel that’s needed for transportation, and a consensus is growing that fuel demand for passenger cars could fall as carbon rules go into effect, electric vehicles gain traction and the internal combustion engine gets re-engineered to be dramatically more efficient. Western countries’ growth used to move in lockstep with their energy consumption, but that phenomenon is starting to decouple in advanced economies.

While most big oil companies foresee a day when the world will need less crude, timing when that peak in oil demand will materialize is one of the hottest flashpoints for controversy within the industry. It’s tough to predict because changes to oil demand will hinge on future disruptive technologies, such as batteries in electric cars that will allow drivers to travel for hundreds of miles on a single charge.

Hitting such a plateau would mark the first time that demand has declined even when economies are growing since Col. Edwin Drake jury-rigged a pipe to drill for oil in Pennsylvania in the late 1850s. Yet, for many companies and investors, the question isn’t whether this immense turning point will happen—it’s when.

Getting that timing right will separate the winners from the losers, and it has become a major preoccupation for energy economists and a flashpoint for controversy within the industry.