As the amount of data generated by experimental and computational works in the field of material science has exploded in the past decade, there is a pressing need for the development of advanced data analytics methods to address the “curse” of data overabundance. In this context, machine learning techniques have been increasingly employed in materials research in recent years. In this work, we explore several applications of generative adversarial networks (GAN), a class of emerging machine learning frameworks, to the digital synthesis and enhancement of material microstructure and the accelerated prediction of microstructure evolution. Using physics-based phase-field simulations to provide training data, the deep convolutational GAN (DCGAN) method is employed to generate realistic-looking microstructures resulting from three distinct physical processes: grain growth, spinodal decomposition and dendrite growth during solidification. In the second application, we apply the super-resolution GAN (SRGAN) method to upsample low-resolution microstructure images to restore the structural details. A multi-level SRGAN scheme is developed to enable an upscaling factor of 16x with acceptable tolerance, which significantly reduces the data sampling need for both experiments and computational modeling. Finally, combining recurrent neural networks (RNN) with DCGAN and SRGAN, we demonstrate a hybrid machine learning model for predicting microstructure evolution. Trained by physics-based simulations, the hybrid model is capable of making reliable predictions at only a small fraction of computational cost by representing the microstructure on coarse mesh grids and increasing the time step size. Our work showcases the significant promise of GAN-related machine learning techniques for materials microstructure analysis and prediction to accelerate materials design and discovery.