The original Brunel tunnel was the world's first under a river; it's now part of the East London Line (closed till the Olympics).
The underground builders thought they were digging well under the river but they had to close the Bakerloo line for months a few years back because the water had washed away a lot of the riverbed above it and it was starting to leak, as I recall.
That's the trouble with London Underground: it was the world's first so they were never able to learn from anyone else's mistakes, they had to make them themselves. New York, for instance, realised that double tracks would be more practical for when you had to repair lines; LU have to shut down at night to allow maintenance, New York doesn't.
The shield's just a shield: you dig more tunnel in front of it, then move it along and line the new bit of tunnel behind it with bricks. It's complicated because the shield comes in sections; but the principle's the same.