Before the Macondo oil spill of 2010, which claimed the job of its former chief executive Tony Hayward, BP was unquestionably the most important company in Britain.
Its dividends accounted for £1 in every £6 of income received by the pension funds managing the retirement savings of tens of millions of Britons.
Its financial health concerned just about everyone in Britain with a life policy, a private sector pension or a stocks and shares Isa, not to mention millions of savers overseas.
Yet the company came close to death as a result of the spill in the Gulf of Mexico.
It has had to set aside some $63bn to meet claims resulting from the explosion on the Deepwater Horizon drilling rig.
Even for a company of BP's size and financial muscle, this was a colossal sum of money. It met these obligations by a sale of assets that continues to this day and by what Brian Gilvary, the company's chief financial officer, describes as financial "gymnastics".
Just as BP was grappling with that, it faced another crisis. It found itself having to negotiate over the future of TNK-BP, Russia's third-largest oil producer, which was a joint venture between it and a group of Russian oligarchs.
The dispute became so unpleasant that at one point TNK-BP's then chief executive Bob Dudley, who succeeded Mr Hayward in 2010, was forced into hiding. Eventually, the Kremlin stepped in, overseeing a takeover of TNK-BP by the state-owned oil producer, Rosneft, in which BP retained a 20% stake. That battle alone would also have pushed to the limit many ordinary companies.
And then, once BP had got to grips with those two huge issues, the oil price collapsed. From $115 a barrel in June 2014, it slumped to just $27 in January last year, blowing a hole in the profitability not only of BP but all the major oil producers.
However, at a time when it was having to reshape its portfolio to deal with the costs of Macondo and commit capital to new exploration and production assets, the threat to BP's profitability was greater than it was to its rivals like Exxon Mobil, Royal Dutch Shell, Chevron and Total.
That is why today's results from BP, for the three months to the end of September, are of such significance.
The company has been invited on numerous occasions since 2010 to state that it had turned a corner and put the Macondo disaster behind it. Today is the first time it has said, yes, perhaps we have turned a corner and, in Dr Gilvary's words, suggested it is approaching conditions that might be described as "normality".
The proof of that is the company's decision to start buying back its shares.
In the aftermath of Macondo, BP sought to save money by issuing dividends in the form of 'scrip' – new shares – rather than paying them in cash. Buying back those shares is a signal that it is confident it is now generating sufficient free cash flow not only to meet its financial obligations – its payments relating to Macondo will still be $1 billion a year from 2019 all the way out to 2032, while it has net debt of almost $40bn – but also to carry on investing in the discovery and exploitation of new oil and gas reserves.
This feels like a significant moment in the recent history of BP. From a near-death experience, it looks to be back on an even keel, provided crude prices do not tank again.Let's