Following the widespread use of deep learning for genomics, deep generative modeling is also becoming a viable methodology for the broad field. Deep generative models (DGMs) can learn the complex structure of genomic data and allow researchers to generate novel genomic instances that retain the real characteristics of the original dataset. Aside from data generation, DGMs can also be used for dimensionality reduction by mapping the data space to a latent space, as well as for prediction tasks via exploitation of this learned mapping or supervised/semi-supervised DGM designs. In this review, we briefly introduce generative modeling and two currently prevailing architectures, we present conceptual applications along with notable examples in functional and evolutionary genomics, and we provide our perspective on potential challenges and future directions.