Prostate cancer (PCa) is the second most common cancer in men and has a significant health and social burden, necessitating advances in early detection, prognosis, and treatment strategies. Improvement in medical imaging has significantly impacted early PCa detection, characterization, and treatment planning. However, with an increasing number of patients with PCa and comparatively fewer PCa imaging experts, interpreting large numbers of imaging data is burdensome, time-consuming, and prone to variability among experts. With the revolutionary advances of artificial intelligence (AI) in medical imaging, image interpretation tasks are becoming easier and exhibit the potential to reduce the workload on physicians. Generative AI (GenAI) is a recently popular sub-domain of AI that creates new data instances, often to resemble patterns and characteristics of the real data. This new field of AI has shown significant potential for generating synthetic medical images with diverse and clinically relevant information. In this narrative review, we discuss the basic concepts of GenAI and cover the recent application of GenAI in the PCa imaging domain. This review will help the readers understand where the PCa research community stands in terms of various medical image applications like generating multi-modal synthetic images, image quality improvement, PCa detection, classification, and digital pathology image generation. We also address the current safety concerns, limitations, and challenges of GenAI for technical and clinical adaptation, as well as the limitations of current literature, potential solutions, and future directions with GenAI for the PCa community.