Miniaturized minimally-invasive implants with wireless power and communication links have the potential to enable closed-loop treatments and precise diagnostics. As with wireless power transfer, robust wireless communication between implants and external transceivers presents challenges and tradeoffs with miniaturization and increasing depth. Both link efficiency and available bandwidth need to be considered for communication capacity. This paper analyzes and reviews active electromagnetic and ultrasonic communication links for implants. Example transmitter designs are presented for both types of links. Electromagnetic links for mm-sized implants have demonstrated high data rates sufficient for most applications up to Mbps range; nonetheless, they have so far been limited to depths under 5 cm. Ultrasonic links, on the other hand, have shown much deeper transmission depths, but with limited data rate due to their low operating frequency. Spatial multiplexing techniques are proposed to increase ultrasonic data rates without additional power or bandwidth.