Generative artificial intelligence (AI), including GANs, VAEs, and diffusion models, is increasingly used for synthesizing and enhancing medical images, helping address challenges such as limited data, expensive acquisition, and rare disease representation. This systematic review examines studies on generative AI methods for MRI, CT, X-ray, and pathology image synthesis from 2017 to 2026, focusing on synthesis tasks, evaluation strategies, and clinical utility. A PRISMA 2020-compliant search of PubMed, IEEE Xplore, Scopus, and Web of Science identified peer-reviewed research on generative models for medical image synthesis, augmentation, harmonization, or cross-modality translation. Findings show a shift from GAN-based methods to diffusion models post-2022, with MRI and CT studies emphasizing cross-modality translation, and X-ray and pathology studies focusing on augmentation and diagnostic utility. Despite GANs' continued dominance, diffusion models are gaining traction for improving image fidelity and diversity. However, evaluation practices remain inconsistent, with limited inclusion of clinically relevant assessments. This review follows PRISMA 2020 guidelines and provides a narrative synthesis of the evidence.