Radiating wireless power transfer (WPT) brings forth the possibility to cost-efficiently charge wireless devices without requiring a wiring infrastructure. As such, it is expected to play a key role in the deployment of limited-battery communicating devices, as part of the 6G enabled Internet-of-Everything (IoE) vision. To date, radiating WPT technologies are mainly studied and designed assuming that the devices are located in the far-field region of the power radiating antenna, resulting in a relatively low energy transfer efficiency. However, with the transition of 6G systems to mmWave frequencies combined with the usage of large-scale antennas, future WPT devices are likely to operate in the radiating near-field (Fresnel) region. In this article, we provide an overview of the opportunities and challenges which arise from radiating near-field WPT. In particular, we discuss about the possibility to realize beam focusing in near-field radiating conditions, and highlight its possible implications for WPT in future {IoE} networks. Besides, we overview some of the design challenges and research directions which arise from this emerging paradigm, including its simultaneous operation with wireless communications, radiating waveform considerations, hardware aspects, and operation with typical antenna architectures.