Radiation source identification plays a pivotal role in modern communication, radar surveillance, and electronic warfare, aiming to rapidly and accurately localize and classify diverse emitters within complex electromagnetic environments for spectrum management, security monitoring, and battlefield situational awareness. Conventional time-domain, frequency-domain, and time–frequency signal-processing techniques, together with machine-learning algorithms based on handcrafted features, struggle to capture the coupled amplitude–phase information of signals under high noise, low signal-to-noise ratio (SNR), and multipath interference. Complex-valued neural networks (CVNNs) directly model in-phase/quadrature (I/Q) data in the complex domain, enabling complete amplitude–phase representation and markedly improving recognition accuracy and interference immunity in low-SNR settings. This paper reviews the state of the art in CVNN-based radiation source identification. First, it surveys innovations in complex-valued convolutional neural networks (CV-CNNs) for time-frequency image feature extraction and lightweight model compression. Next, it examines the use of complex-valued recurrent neural networks (CV-RNNs) for temporal feature modeling and incremental identification. The paper then explores how attention mechanisms, self-supervised learning, and adversarial training can be integrated into complex-domain frameworks to enhance model generalization and robustness. Finally, it analyzes current technical bottlenecks—including parameter initialization, training stability, computational cost, and few-shot transfer learning—and outlines future research directions such as lightweight architectures for edge devices, complex-domain data augmentation, and multimodal fusion, with the goal of improving the real-time performance and reliability of radiation source identification systems.