Well, that problem has been solved, to a great degree, and the solution applied with varying results in other formations and basins.
There are still more places we know there is oil (oil shale, for instance). --other formations which will not lend themselves to the methodology of today, but people are still working on the right combination of method and technology to extract that oil, too.
I don't think we are anywhere near the peak, but I think there will be temporally localized highs and lows in supply, driven by a combination of market, technology, and need.
Part of the problem solving, including advancements of technology, get driven by relatively higher prices.
The concern of running out of cheap oil is more real than running out of producible oil. Competing energy sources help drive this.