Artificial intelligence (AI) is pivotal in advancing fifth-generation (5G)-Advanced and sixth-generation systems, capturing substantial research interest. Both the 3rd Generation Partnership Project (3GPP) and leading corporations champion AI's standardization in wireless communication. This piece delves into AI's role in channel state information (CSI) prediction, a sub-use case acknowledged in 5G-Advanced by the 3GPP. We offer an exhaustive survey of AI-driven CSI prediction, highlighting crucial elements like accuracy, generalization, and complexity. Further, we touch on the practical side of model management, encompassing training, monitoring, and data gathering. Moreover, we explore prospects for CSI prediction in future wireless communication systems, entailing integrated design with feedback, multitasking synergy, and predictions in rapid scenarios. This article seeks to be a touchstone for subsequent research in this burgeoning domain.