This article presents a novel multi-functional system for a sixth-generation (6G) wireless network with integrated sensing, communication, and powering (ISCAP), which unifies integrated sensing and communication (ISAC) and wireless information and power transfer (WIPT) techniques. The multi-functional ISCAP network promises to enhance resource utilization efficiency, reduce network costs, and improve overall performance through versatile operational modes. Specifically, a multi-functional base station (BS) can enable multi-functional transmission, by exploiting the same radio signals to perform target/environment sensing, wireless communication, and wireless power transfer (WPT), simultaneously. Besides, the three functions can be intelligently coordinated to pursue mutual benefits,i.e., wireless sensing can be leveraged to enable light-training or even training-free WIPT by providing side-channel information, and the BS can utilize WPT to wirelessly charge low-power devices for ensuring sustainable ISAC. Furthermore, multiple multi-functional BSs can cooperate in both transmission and reception phases for efficient interference management, multi-static sensing, and distributed energy beamforming. For these operational modes, we discuss the technical challenges and potential solutions, particularly focusing on the fundamental performance tradeoff limits, transmission protocol design, as well as waveform and beamforming optimization. Finally, interesting research directions are identified.