Walking is a fascinating invention of nature. It is versatile, flexible and perfectly adapted to a natural environment. Walking in its various realizations enables the biological systems to have access to all natural structures of the earth. Walking realizes motion, and motion with motion planning is the basis for intelligence, as modern biologists say. If intelligence is defined as the ability to deal with unknown and new situations then biological motion, both mental and physical, can be considered as a manifestation of intelligence. Walking has been investigated by engineers for 20-30 years, although before that time numerous trials had been made to realize some mechanisms with walking capabilities. Nowadays the computer age and a large variety of sophisticated technologies give walking machine realizations a high probability of success, which can best be seen in Japan. My group at the Technical University of Munich started in 1989 to design and to realize walking machines, partly in cooperation with neurobiologists specialized in biological walking problems. The presentation will touch on some problems connected with machine walking, especially in the fields of design, dynamics, control and stabilization. It will also discuss some of the open questions connected with walking, especially stabilization problems. Finally, the chances of walking machines will be discussed.