Progress in the detection and study of continuous nanohertz gravitational wave sources

In recent years, pulsar timing array (PTA) experiments have made substantial progress in probing the nanohertz gravitational wave background, propelling the search for continuous gravitational waves (CGWs) from supermassive binary black holes (SMBBHs) to the forefront of astrophysical research. This review systematically synthesizes key advancements in the field. On the theoretical front, a comprehensive framework has emerged for modeling SMBBH dynamical evolution and population distributions, incorporating semi-empirical models, post-processing techniques, and phenomenological approaches that provide robust foundations for observational studies. Observationally, CGW searches have become an integral component of standard PTA data analysis pipelines, with continual improvements in timing precision and noise characterization. Nonetheless, statistically significant CGW detections have yet to be realized. With increasing observational time spans and improving data quality, PTAs are poised to achieve the first robust detection of CGWs from SMBBHs in the near future. Sustained progress in this field will be driven by integrated efforts, including joint analyses of continuous and stochastic signals, coordinated multi-band observations with future space-based detectors (such as LISA, Taiji, and TianQin), and multi-messenger approaches that incorporate electromagnetic counterparts. Collectively, these developments promise to revolutionize our understanding of SMBBH formation and evolution, enable novel tests of gravitational physics, and offer new insights into early-universe cosmology.