Generative Adversarial Network (GAN), deemed as a powerful deep-learning-based silver bullet for intelligent data generation, has been widely used in multi-disciplines. Furthermore, conditional GAN (CGAN) introduces artificial control information on the basis of GAN, which is more practical for many specific fields, though it is mostly used in domain transfer. Researchers have proposed numerous methods to tackle diverse tasks by employing CGAN. It is now a timely and also critical point to review these achievements. We first give a brief introduction to the principle of CGAN, then focus on how to improve it to achieve better performance and how to evaluate such performance across the variants. Afterward, the main applications of CGAN in domain transfer are presented. Finally, as another major contribution, we also list the current problems and challenges of CGAN.