We present the NanoPeers architecture paradigm, a peer-to-peer network of lightweight devices, lacking all or most of the capabilities of their computer-world counterparts. We identify the problems arising when we apply current routing and searching methods to this nano-world, and present some initial solutions, using a case study of a sensor network instance; Smart Dust. Furthermore, we propose the P2P Worlds framework as a hybrid P2P architecture paradigm, consisting of cooperating layers of P2P networks, populated by computing entities with escalating capabilities. Our position is that (i) experience gained through research and experimentation in the field of P2P computing, can be indispensable when moving down the stair of computing capabilities, and that (ii) the proposed framework can be the basis of numerous real-world applications, opening up several challenging research problems.