In the last few years, there has been remarkable progress in deep generative modeling. However, the learned models are noticeably inaccurate w.r.t. to the underlying data distribution, as evident from downstream metrics that compare statistics of interest across the true and generated data samples. This bias in downstream evaluation can be attributed to imperfections in learning ("model bias") or be propagated due to the bias in the training dataset itself ("dataset bias"). In this talk, I will present an importance weighting approach for mitigating both these kinds of biases of generative models. Our approach assumes only ‘black-box' sample access to a generative model and is broadly applicable to both likelihood-based and likelihood-free generative models. Empirically, we find that our technique consistently improves standard goodness-of-fit metrics for evaluating the sample quality of state-of-the-art deep generative models, suggesting reduced bias. We demonstrate its utility on representative applications in a) data augmentation, b) model-based policy evaluation using off-policy data, and c) permutation-invariant generative modeling of graphs. Finally, I will present some recent work extending these ideas to fair data generation in the presence of biased training datasets.