Wireless power transfer (WPT) techniques have been utilized in various biomedical applications to overcome the challenges of battery capacity and lifetime, and high-cost surgical interventions, using biomedical implants (BMIs) and biomedical sensors (BMSs), including deep brain stimulators, capsule endoscopes, pacemakers, and cardiac monitoring sensors. In this article, near-field WPT methods in BMIs and BMSs, including magnetic resonator coupling (MRC), inductive coupling (IC), and capacitive coupling (CC), are reviewed, and some biomedical applications of these methods are highlighted. The applications of WPT have been explored in recent years to enhance the major performance metrics of BMIs. The main topologies of MRC-WPT are presented, and the main mathematical models related to each type were extracted from previous studies and detailed here. Additionally, the main performance metrics and results achieved, along with their suggested biomedical applications, are summarized in a comparison table. Some challenges and limitations of using WPT in the biomedical field and suggestions for improving the efficiency of WPT for biomedical applications are also discussed. Furthermore, future trends in WPT-based BMIs are also highlighted.