Recent advancements in wave computing using metasurfaces are poised to transform wireless communications by enabling high-speed, energy-efficient, and highly parallelized signal processing. These capabilities are essential to meet the ultra-high data rates of up to 1 terabit per second and minimal latency as low as 1 millisecond required by next-generation wireless networks. Diverging from traditional digital processing, wave computing adopts continuous analog signals to foster innovative functions such as over-the-air computation, integrated sensing and communications, computational electromagnetic imaging, and physical-layer security. This article explores the potential of reconfigurable multi-functional metasurfaces in wave computing, emphasizing their pivotal role in facilitating seamless communications and addressing the escalating computational demands for sixth generation (6G) networks. As artificial intelligence has become one of the most prominent and rapidly advancing fields of research over the last decade, we also introduce a wave-domain-based machine learning approach aimed at achieving power-efficient, fast training and computation. Future research directions are discussed, underscoring how metasurface-based systems can merge computation with communication to innovate components of 6G networks, thus creating smarter, faster, and more adaptable wireless infrastructures.