Wireless power transfer (WPT) is an emerging paradigm that will enable using wireless to its full potential in future networks, not only to convey information but also to deliver energy. Such networks will enable trillions of future low-power devices to sense, compute, connect, and energize anywhere, anytime, and on the move. The design of such future networks brings new challenges and opportunities for signal processing, machine learning, sensing, and computing. The objective is to make the best use of the RF radiations, spectrum, and network infrastructure to provide cost-effective and real-time power supplies to wireless devices and enable wireless-powered applications. In this paper, we first review recent signal processing techniques to make WPT and wireless information and power transfer (WIPT) as efficient as possible. Topics include high-power amplifier and energy harvester nonlinearities, active and passive beamforming, intelligent reflecting surfaces, receive combining with multi-antenna harvester, modulation, coding, waveform, large-scale (massive) multiple-input multiple-output (MIMO), channel acquisition, transmit diversity, multi-user power region characterization, coordinated multipoint, and distributed antenna systems. Then, we overview two different design methodologies: the model and optimize approach relying on analytical system models, modern convex optimization, and communication/information theory, and the learning approach based on data-driven end-to-end learning and physics-based learning. We discuss the pros and cons of each approach, especially when accounting for various nonlinearities in wireless-powered networks, and identify interesting emerging opportunities for the approaches to complement each other. Finally, we identify new emerging wireless technologies where WPT may play a key role—wireless-powered mobile edge computing, wireless-powered sensing, and wireless-powered federated learning—arguing WPT, communication, computation, ...