Over the last decade, simultaneous wireless information and power transfer (SWIPT) has become a practical and promising solution for connecting and recharging batterylimited devices, thanks to significant advances in low-power electronics technology and wireless communications techniques. To realize the promised potentials, advanced resource allocation design plays a decisive role for revealing, understanding, and exploiting the intrinsic rate-energy tradeoff capitalizing on the dual use of radio frequency (RF) signals for wireless charging and communication. In this paper, we provide a comprehensive tutorial overview of SWIPT from the perspective of resource allocation design. The fundamental concepts, system architectures, and RF energy harvesting (EH) models are introduced. In particular, three commonly adopted EH models, namely the linear EH model, the nonlinear saturation EH model, and the nonlinear circuit-based EH model are characterized and discussed. Then, for a typical wireless system setup, we establish a generalized resource allocation design framework which subsumes conventional resource allocation design problems as special cases. Subsequently, we elaborate on relevant tools from optimization theory and exploit them for solving representative resource allocation design problems for SWIPT systems with and without perfect channel state information (CSI) available at the transmitter, respectively. The associated technical challenges and insights are also highlighted. Furthermore, we discuss several promising and exciting future research directions for resource allocation design for SWIPT systems intertwined with cuttingedge communication technologies, such as intelligent reflecting surfaces, unmanned aerial vehicle, mobile edge computing, federated learning, and machine learning.