[1] When I was at Intel the 386 was the new hawtness. The first silicon samples powered up and ran which was awesome but at 'full speed' there were some issues that turned out to be related to a clock signal somewhere between the registers and the ALU. The design engineer replaced a metal feature (typical conductors were done in the metal layer) with a polysilicon version which had the effect of slowing down the propagation speed enough to line up the clocks. (it was fortunate it didn't need to go faster which is harder to do :-) These days the device geometries are so small as to require a lot of analysis which I would not enjoy trying to do by "hand".
It's a matter of distance between components on the die, and transistor sizing. At the scale of complex integrated circuits, it's just about guaranteed that an automatic route will do a good job, but stands a good chance of messing a few hotspots up.
I'm not an expert on the algorithms used for automatic routing, but there is some random guessing involved. You can even provide a seed for the random number generator.
More often than not, a hybrid approach is used where the designer gives broad recommendations on where to place components and lets the autorouter go from there.
Then at the end, the designer may go in and tweak some hot spots, or scrap it and start over with a new seed.
I've had times where the auto router for a board gave up because it couldn't complete the routing, ripped everything up and did it by hand. Sure it took longer but the routes were shorter, and I finished routing the board with room to spare.
http://folklore.org/StoryView.py?story=Nybbles.txt
"The Apple II disk controller, designed six months after the Apple II itself was complete, was Steve Wozniak's crowning achievement. His five chip disk controller card out-performed competitive controllers that were four times as expensive by shifting most of the responsibilities from hardware to software. In Woz's approach, the software was responsible for doing all of the encoding and decoding, head stepping, etc. This allowed Woz to improve the capacity and performance over standard techniques."
http://apple2history.org/history/ah05/
For two weeks, he worked late each night to make a satisfactory design. When he was finished, he found that if he moved a connector he could cut down on feedthroughs, making the board more reliable. To make that move, however, he had to start over in his design. This time it only took twenty hours. He then saw another feedthrough that could be eliminated, and again started over on his design. “The final design was generally recognized by computer engineers as brilliant and was by engineering aesthetics beautiful. Woz later said, ‘It’s something you can only do if you’re the engineer and the PC board layout person yourself. That was an artistic layout. The board has virtually no feedthroughs.’