Implantable medical systems for long-term monitoring of bioelectrical activity of the gastrointestinal (GI) tract, known as slow waves, and for treating GI dysmotility and functional disorders through electrical stimulation pulses have emerged over the recent years. These implants construct a bidirectional interface between the clinician and the patient's GI tract, to record and monitor slow waves and to provide electrical therapies. Because of the limited battery life of the implants, wireless power transfer (WPT) is a fundamental requirement to conduct studies and provide treatments for an extended period. Furthermore, the WPT link provides the opportunity to establish near-field data communication over the same link. Currently, there are three main wireless power and data transfer (WPDT) approaches for GI tract implants consisting of resonant inductive, ultrasonic, and capacitive couplings. Each approach provides a tradeoff based on the size of the implant, depth of implantation <i>in vivo</i>, the amount of power received by the implant, and the WPT efficiency. In this review, we present the theory and an overview of the major research works accomplished for each of the aforementioned WPT approaches. In particular, this paper focuses on simultaneous WPDT for systems implanted in the GI tract, while fluctuations of the wireless link efficiency and reliability due to body movements and stomach motility are investigated, and techniques are introduced to improve the WPDT fidelity.