BEAM is an acronym for Biology Electronics Aesthetics and Mechanics.
These robots are ingeniously simple and instead of having complex Microcontroller and programs, BEAM robots use wave generators which are very close to having their stability pulled out by sensors.
Some of the BEAM robots use simple circuits with a capacitor, which after reaching a trigger voltage, causes a Transistor to flip. This circuit will drive a motor for a brief burst of motion, then stop after the capacitor is fully discharged. Such a circuit is a great use of Solar Panels and pretty easy to build.
Legged robots can be built in interesting ways using sine wave combinations offset by 90/180 degrees. If used with Muscle Wire - it means you can get a set of flowing contractions just from the wave generators.
Some people like the idea of taking the BEAM principles, and creating a Horse And Rider Robot - a very interesting proposition indeed.
Mark Tilden owns many copyrights and patents in the BEAM robotics area.
Junkbots, Bugbots and Bots on Wheels: Building Simple Robots with BEAM Technology
Dave Hrynkiw, Mark W. Tilden
This book is an excellent starters guide, and anybody intending to build these robots should have Junkbots on their shelf. I have built some robots based upon these ideas. The book covers tools, techniques, actual robot designs and more.