Intelligent reflecting surface (IRS) is a promising technology for achieving spectrum and energy-efficient wireless networks cost-effectively. Most existing works on IRS have focused on exploiting IRS to enhance the performance of wireless communication or wireless information transmission (WIT), while its potential for boosting the efficiency of radio frequency (RF) wireless energy transmission (WET) still remains largely open. Although IRS-aided WET shares similar characteristics with IRS-aided WIT, they differ fundamentally in terms of design objective, receiver architecture, practical constraints, and so on. In this article, we provide a tutorial overview on how to efficiently design IRS-aided WET systems as well as IRS-aided systems with both WIT and WET, namely, IRS-aided simultaneous wireless information and power transfer (SWIPT) and IRS-aided wireless powered communication network (WPCN), from a communication and signal processing perspective. In particular, we present state-of-the-art solutions to tackle the unique challenges in operating these systems, such as IRS passive reflection optimization, channel estimation, and deployment. In addition, we propose new solution approaches and point out important directions for future research and investigation.