Researchers in the field of biocomputing have, for many years, successfully "harvested and exploited" the natural world for inspiration in developing systems that are robust, adaptable and capable of generating novel and even "creative" solutions to human-defined problems. However, in this position paper we argue that the time has now come for a reassessment of how we exploit biology to generate new computational systems. Previous solutions (the "first generation" of biocomputing techniques), whilst reasonably effective, are crude analogues of actual biological systems. We believe that a new, inherently inter-disciplinary approach is needed for the development of the emerging "second generation" of bio-inspired methods. This new modus operandi will require much closer interaction between the engineering and life sciences communities, as well as a bidirectional flow of concepts, applications and expertise. We support our argument by examining, in this new light, three existing areas of biocomputing (genetic programming, artificial immune systems and evolvable hardware), as well as an emerging area (natural genetic engineering) which may provide useful pointers as to the way forward.