Deep generative models have been recently proposed as modular datadriven priors to solve inverse problems. Linear inverse problems involve the reconstruction of an unknown signal (e.g. a tomographic image) from an underdetermined system of noisy linear measurements. Most results in the literature require that the reconstructed signal has some known structure, e.g. it is sparse in some known basis (usually Fourier or wavelet). Such prior assumptions can be replaced with pre-trained deep generative models (e.g. generative adversarial getworks (GANs) and variational autoencoders (VAEs)) with significant performance gains. This chapter surveys this rapidly evolving research area and includes empirical and theoretical results in compressed sensing for deep generative models.