Generative models provide a well-established statistical framework for evaluating uncertainty and deriving conclusions from large data sets especially in the presence of noise, sparsity, and bias. Initially developed for computer vision and natural language processing, these models have been shown to effectively summarize the complexity that underlies many types of data and enable a range of applications including supervised learning tasks, such as assigning labels to images; unsupervised learning tasks, such as dimensionality reduction; and out-of-sample generation, such as de novo image synthesis. With this early success, the power of generative models is now being increasingly leveraged in molecular biology, with applications ranging from designing new molecules with properties of interest to identifying deleterious mutations in our genomes and to dissecting transcriptional variability between single cells. In this review, we provide a brief overview of the technical notions behind generative models and their implementation with deep learning techniques. We then describe several different ways in which these models can be utilized in practice, using several recent applications in molecular biology as examples.