The rapid evolution of forthcoming sixth-generation (6G) wireless networks necessitates the seamless integration of artificial intelligence (AI) with wireless communications to support emerging intelligent applications that demand both efficient communication and robust learning performance. This dual requirement calls for a unified framework of integrated learning and communication (ILAC), where AI enhances communication through intelligent signal processing and adaptive resource management, while wireless networks support AI model deployment by enabling efficient and reliable data exchanges. However, achieving this integration presents significant challenges in practice. Communication constraints, such as limited bandwidth and fluctuating channels, hinder learning accuracy and convergence. Simultaneously, AI-driven learning dynamics, including model updates and task-driven inference, introduce excessive burdens on communication systems, necessitating flexible, context-aware transmission strategies. Finally, we present a case study on a cost-to-performance optimization problem, where task assignments, model size selection, bandwidth allocation, and transmission power control are jointly optimized, considering computational cost, communication efficiency, and inference accuracy. Leveraging the Dinkelbach and alternating optimization algorithms, we offer a practical and effective solution to achieve an optimal balance between learning performance and communication constraints.