The rapid development of chargeable devices has caused a great deal of interest in efficient and stable wireless power transfer (WPT) solutions. Most conventional WPT technologies exploit outdated electromagnetic field control methods proposed in the 20th century, wherein some essential parameters are sacrificed in favour of the other ones (efficiency vs. stability), making available WPT systems far from the optimal ones. Over the last few years, the development of novel approaches to electromagnetic field manipulation has enabled many up-and-coming technologies holding great promises for advanced WPT. Examples include coherent perfect absorption, exceptional points in non-Hermitian systems, non-radiating states and anapoles, advanced artificial materials and metastructures. This work overviews the recent achievements in novel physical effects and materials for advanced WPT. We provide a consistent analysis of existing technologies, their pros and cons, and attempt to envision possible perspectives.