The spring reverbs work by splitting your signal and sending part through a tube driver, then through a transducer to convert the electrical signal to mechanical energy, which moves down the springs. The mechanical energy moves slower than the electrical signal, so that signal is delayed. At the end of the reverb springs, the mechanical energy is changed back to an electrical signal with another transducer. The signal is pretty weak by this time, so it is amplified again and combined with the original signal to produce the reverb sound. Some real old units used an oil-filled tank instead of springs, which produced a similar effect (I've never heard one).
The original digital reverbs split the analog signal, converted one part to a digital signal and then stored the digital signal in a "Bucket-Brigade" memory bank for the desired time. The stored digital signal was converted back to analog and the two signals were recombined to make the reverb effect. I believe that a lot of stomp boxes still use this basic technology, but the manufacturer that makes the Bucket Brigade memory is stopping production. This may effect the price and availability of some stomp boxes.
A lot of new reverbs use a Digital Signal Processing (DSP) chip, which is a microprocessor similar to the processor used in your PC or Mac. The DSP system has additional circuitry and commands to handle analog to digital signal conversion and the return to analog. Once the signal is in a digital format, it can be manipulated by software programs in many ways - this is how the new modeling amps and pedals produce their wide tonal variations.
Hope this helps.

[This message has been edited by Jon68 (edited 09-08-2000).]