The rapid advancement of underwater wireless communication technologies is critical to unlocking the full potential of marine resource exploration and environmental monitoring. This paper reviews recent progress in three primary modalities: underwater acoustic communication, radio frequency (RF) communication, and underwater optical wireless communication (UWOC), each designed to address specific challenges posed by complex underwater environments. Acoustic communication, while effective for long-range transmission, is constrained by ambient noise and high latency; recent innovations in noise reduction and data rate enhancement have notably improved its reliability. RF communication offers high-speed, short-range capabilities in shallow waters, but still faces challenges in hardware miniaturization and accurate channel modeling. UWOC has emerged as a promising solution, enabling multi-gigabit data rates over medium distances through advanced modulation techniques and turbulence mitigation. Additionally, bio-inspired approaches such as electric field communication provide energy-efficient and robust alternatives under turbid conditions. This paper further examines the practical integration of these technologies in underwater platforms, including autonomous underwater vehicles (AUVs), highlighting trade-offs between energy efficiency, system complexity, and communication performance. By synthesizing recent advancements, this review outlines the advantages and limitations of current underwater communication methods and their real-world applications, offering insights to guide the future development of underwater communication systems for robotic and vehicular platforms.