This paper presents the VLEIBot^* (Very Little Eel-Inspired roBot), a 45-mg/23-mm^3 microrobotic swimmer that is propelled by a bioinspired anguilliform propulsor. The propulsor is excited by a single 6-mg high-work-density (HWD) microactuator and undulates periodically due to wave propagation phenomena generated by fluid-structure interaction (FSI) during swimming. The microactuator is composed of a carbon-fiber beam, which functions as a leaf spring, and shape-memory alloy (SMA) wires, which deform cyclically when excited periodically using Joule heating. The VLEIBot can swim at speeds as high as 15.1mm * s^{-1} (0.33 Bl * s^{-1}}) when driven with a heuristically-optimized propulsor. To improve maneuverability, we evolved the VLEIBot design into the 90-mg/47-mm^3 VLEIBot^+, which is driven by two propulsors and fully controllable in the two-dimensional (2D) space. The VLEIBot^+ can swim at speeds as high as 16.1mm * s^{-1} (0.35 Bl * s^{-1}), when driven with heuristically-optimized propulsors, and achieves turning rates as high as 0.28 rad * s^{-1}, when tracking path references. The measured root-mean-square (RMS) values of the tracking errors are as low as 4 mm.