This one of the classic human error examples. With the problems in Japan with the Fukushima Daiichi following the earth quake and tsunami, the BBC has given a good summary of what happened at 4am on Wednesday 28 March, 1979.
A relatively routine malfunction in a non-nuclear system caused a relief valve to open, releasing coolant from the core. The valve should have closed after a moment, but it didn't, and a large volume of coolant escaped.
There was no straightforward way for the plant's operators to know that the valve was the problem. No instrument on their control panel indicated whether it was open or closed.
Operators knew something was going wrong, though - alarms sounded and lights were flashing.
They mistakenly diagnosed the issue as being too much coolant in the pressuriser and shut off the emergency core cooling system, the first in a series of missteps that escalated the crisis.
"In not knowing what was going wrong and taking exactly the wrong action, they exacerbated the problem by orders of magnitude," says J Samuel Walker, a historian who worked for many years for the Nuclear Regulatory Commission (NRC), the US atomic agency and nuclear watchdog.
Operators worked furiously for days to minimize the meltdown.
It wasn't until 1985, when sophisticated cameras were sent into the core, that authorities understood the enormous extent of the meltdown.
The TMI disaster took over 12 years to clean up, at a cost of about $973m (£605m).
Fortunately, little radiation was released, and multiple studies have shown no serious health impacts.
There was no documented increase in cancers. Links between TMI and problems with livestock in the area, including deaths and reproductive issues, have not been proven.