Following the persistent evolution of terrestrial 5G wireless systems, a new field of underwater communication has emerged for various related applications like environmental monitoring, underwater mining, and marine research. However, establishing reliable high-speed underwater networks remains notoriously difficult due to the severe RF attenuation in conductive seawater, which strictly limits range coverage. In this article, we focus on a comprehensive review of different antenna types for future underwater communication and sensing systems, evaluating their performance and suitability for Autonomous Underwater Vehicles (AUVs). We critically examine and compare distinct antenna technologies, including Magnetic Induction (MI) coils, electrically short dipoles, wideband traveling wave antennas, printed planar antennas, and novel magnetoelectric (ME) resonators. Specifically, these antennas are compared in terms of physical footprint, operating frequency, bandwidth, and realized gain, revealing the trade-offs between miniaturization and radiation efficiency. Our analysis aims to identify the benefits and weaknesses of the different antenna types while emphasizing the necessity of innovative antenna designs to overcome the fundamental propagation limits of the underwater channel.