As robotics advances, swimming robots can potentially be used for monitoring the ocean, performing tasks in remote locations, and other practical applications. Looking towards nature for inspiration can address some of the grand challenges of robotics, such as improved dexterity and adaptive abilities in unstructured environments. This work presents examples of bioinspired swimming robots using approaches that combine laboratory and field experiments, theoretical models, and computational fluid dynamics. First, we demonstrate a biohybrid robot that uses a microelectronic system to induce swimming in live jellyfish in the laboratory and ocean. Using entirely synthetic materials, we also address how bioinspired sharkskin surfaces and robotic fish fins can improve the performance envelope of vehicles. Future applications include improving swimming speeds, efficiencies, and antifouling properties for enhanced persistence. These examples provide a strong foundation for continued work to design and implement robots for real-world applications.