The story of oil is so identical with John D. Rockefeller. I think it's wrong to say that he started everything. However, no doubt he helped build the industry. At the time, people didn't know the use of crude oil more than to light houses i.e. kerosene. However, a sloppy mistake could burn houses. That's where the name came from: Rockefeller made it standard and hence safer.
He transported barrels of oil by train. At one point, the train companies (one of them owned by Thomas Scott, Carnegie's mentor) agreed to raise the cost. This drove Rockefeller mad. But genius he was, he thought of transporting oil through pipes instead. The idea changed the industry. Oil no longer filled train's compartments. On the other hand, train companies suffered. Some even went bankrupt. (But it's hard to say; railroads were overbuilt that time).
Later on, through research and experimenting, Rockefeller realized the huge potential in refining crude oil. He foresaw that when Ford hadn't come to scene yet.
Standard oil grew bigger than ever. This drew public attention. When Teddy Roosevelt became the president, Standard Oil was charged of being a monopoly under the antitrust law. The company was broken into 34 companies across the states. However, decentralization just made this conglomerate ever stronger and bigger. In the 90s, some of its successors like Exxon and Mobil merged and formed new companies e.g. ExxonMobil, Chevron, etc. Today these companies are among the largest companies by revenue.