The efficiency of wireless information and power transfer (WIPT) systems requires an essential reevaluation and rethinking of the entire transceiver chain, which is characterized by a bottom-up multi-layer design approach. In this paper, we introduce and describe the key design layers: i) "Mathematical modeling", associated with the investigation of mathematical models for the wireless power transfer process, ii) "Information-theoretic limits", which refers to the fundamental limits of the WIPT channel, iii) "Link design", corresponding to signal processing techniques that make WIPT feasible, iv) "System-level perspective", which studies the developed WIPT techniques from a macroscopic system-level point-of-view, and v) "Experimental studies", that refers to real-world implementation of WIPT systems. These layers are well-connected and their interplay is imperative for the effective design of WIPT systems. Specific case studies are discussed, which demonstrates the interdisciplinary nature of the aforementioned multi-layer design framework.