The Terahertz (THz) band (0.1-10 THz) has emerged as a critical frontier for future communication systems, offering ultra-wide bandwidths that enable Terabits-per-second (Tbps) wireless links and high-precision sensing and imaging. However, practical deployment of THz systems is hindered by unique challenges, including intricate channel characteristics, high-dimensional and large-scale optimization problems, and highly dynamic network environments. Artificial Intelligence (AI) serves as a transformative enabler to address these challenges, providing robust capabilities for precise modeling, advanced signal processing, complex optimization, real-time decision-making, and prediction, among others. Reciprocally, the unprecedented bandwidth and high-resolution sensing capabilities of THz networks provide a promising physical infrastructure for AI, facilitating training, inference, and data collection. This survey presents a systematic and comprehensive overview of AI-driven solutions across the entire THz communication network and the symbiosis of AI and THz networks. To begin with, a foundational overview of AI technologies tailored for wireless communications is presented. Subsequently, AI-based innovations are investigated, spanning from hardware design, channel modeling, physical layer optimization, up to higher-layer network protocols and advanced THz services, including mobile edge computing and sensing-empowered applications. In parallel, the capacity of THz networks to serve AI is examined, underscoring a profound paradigm shift towards a mutual symbiosis where AI and THz co-evolve and empower each other. Finally, by synthesizing these state-of-the-art advancements and identifying open research directions, this survey highlights the potential of AI in copilot with development of THz communication systems.