Generative modeling has emerged as a promising direction in computational pathology, offering capabilities such as data-efficient learning, synthetic data augmentation, and multimodal representation across diverse diagnostic tasks. This review provides a comprehensive synthesis of recent progress in the field, organized into four key domains: image generation, text generation, multimodal image-text generation, and other generative applications, including spatial simulation and molecular inference. By analyzing over 150 representative studies, we trace the evolution of generative architectures from early generative adversarial networks to recent advances in diffusion models and foundation models with generative capabilities. We further examine the datasets and evaluation protocols commonly used in this domain and highlight ongoing limitations, including challenges in generating high-fidelity whole slide images, clinical interpretability, and concerns related to the ethical and legal implications of synthetic data. The review concludes with a discussion of open challenges and prospective research directions, with an emphasis on developing unified, multimodal, and clinically deployable generative systems. This work aims to provide a foundational reference for researchers and practitioners developing and applying generative models in computational pathology.