> I must admit, I've always wondered how the hell ABS actually works.

A speed sensor on each wheel, if one drops too quickly compared to the 
others, or they all drop too quickly than what is "usually possible" a 
solenoid is opened that releases the brake pressure until the wheels speeds 
are back to normal, then the solenoid is closed.  The process might then 
repeat if the driver is still pressing the brake pedal hard - this is the 
"pulsing" sensation you feel.

Note that modern cars are much more complex, with ABS being part of a much 
larger control system, capable of regulating the braking force to each 
individual wheel (to allow each wheel to be giving the maximum stopping 
power, and to prevent skids, wheel-spin etc).

> But not as much as power steering. This, as far as I can tell, should be 
> logically impossible. And yet it apparently works. How baffling!

There's a part in the steering system that twists or bends by a specific 
amount depending on how hard you tug at the wheel.  A set of valves then 
controls some pressurised hydraulics based on how much force you are putting 
into the wheel, which helps you steer.

Newer cars have a torque transducer and an electric motor with some clever 
software.  This saves on fuel as there is no hydraulic compressor having to 
be run the whole time (usually you only need power assist at low speeds).

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