Through our experience in building a number of behavior-based robots in the past few years, we feel strongly that there must be a fundamental revision in approach to robotics. Such a revision must happen particularly with respect to mobile robots operating in dynamic real life environments. However, since pressure exists to make even stationary robots operate in dynamic environments with increasingly more encounters with demands for flexible operations, abrupt changes in tasks, and perturbations, it appears a similar change in approach to robotics as a whole needs to be considered. The traditional approach has been perfected over the past few decades for mostly stationary manufacturing robots which operate in a clearly definable (i.e., closed) world. This approach will not suffice in many emerging robot application areas such as robots for the service industry, the handicapped, and entertainment. It is necessary to cope with operational parameters and characteristics that are significantly more demanding, not only in technology, but also in science and philosophy. A change in approach to robotics rooted in a non-Cartesian frame of thought will have to be realized. The issue is especially challenging to those practitioners who are well-established and active in traditional robotics as the conventional robot is nothing other than a “Descartes Machine”, and to alter one's basic mannerism is always very difficult to do. A short summary of the characteristics of non-Cartesian robots and several of our attempts to develop such robots are described.