Wireless federated learning (FL), which allows edge devices to perform local deep/machine learning (DL/ML) training and further aggregates the locally trained models from them via radio channels, establishes a promising framework for enabling various DL/ML-based services in future B5G/6G networks. Despite respecting the data privacy, periodically performing the local model training is not friendly to energy-constrained edge devices and degrades the sustainability and performance of FL services. In this article, motivated by the advanced simultaneous wireless information and power transfer (SWIPT), we propose a framework of SWIPT-empowered wireless FL that can provide over-the-air wireless power transfer in parallel with the transmission of global/local models. We present the key approaches of leveraging SWIPT for FL with their advantages illustrated. The practical challenging issues in reaping the benefits of integrating SWIPT are then discussed and we also provide the potential solutions to address these issues. A representative case study of FL via SWIPT is presented to validate the advantages of exploiting SWIPT. To this end, we present a joint design of SWIPT policy and the client-scheduling for FL, which is firstly formulated as a finite horizon dynamic optimization problem and then is solved by an actor-critic-based deep reinforcement learning algorithm. We finally articulate some potential open future directions regarding the SWIPT-empowered wireless FL.