LDR

[rockgardenlove]

Whats the point in using an LED and LDR? 

[varialbender]

The combination of the two, making an optoisolator, are magical.
In some phasers, you send your oscillator signal to the LED portion and the resistor mimics this with resistance, moving the notches back and forth in the frequency spectrum.
In some compressors, an envelope signal is sent to the LED, and the resistor controls the output volume.
I think they're mostly appreciated for the minimal noise. FETs in a phaser are known to distort and get noisy.
The downside is that they're not as fast as FETs. You can't get LEDs to oscillate at good audio frequencies, for example.

[Mark Hammer]

One of the advantages to using an LED/LDR combination is that the portion of the circuit meant to do the "driving" (controlling) is isolated electronically from the audio part of the circuit, because the LDR and LED are only "connected" by light.

As well, since it is "just a resistor", there are places you can insert an LDR into a circuit that you can't insert other types of control elements.  For example, suppose you had some bizarre circuit that adjusted the biasing of a JFET dynamically.  You could do it with an LDR, but you can't stick a FET in the same place to bias another FET.

As for speed, a great many LDRs are not fast enough to respond to audio frequency changes (i.e., changing resistance upwards or downwards at a rate faster than 20hz), but some are, and others are happy to make small changes at fast speeds, just not huge resistance changes.  In contrast, FETs will always respond at audio frequencies, no matter which one you pick.

There are lots of ways to use LDRs.  Shining an LED on it is certainly one.  Many older Morley pedals would use an LDR, a small incandescent bulb, and a "shutter".  As you moved the pedal mechanisms forward and backward, it would physically block and let through the light from the bulb by sliding the butter over the LDR.