We argue that deep learning provides a promising avenue for taming the curse of dimensionality in quantitative economics. We begin by exploring the unique challenges posed by solving dynamic equilibrium models, especially the feedback loop between individual agents’ decisions and the aggregate consistency conditions required by equilibrium. Following this, we introduce deep neural networks and demonstrate their application by solving the stochastic neoclassical growth model. Next, we compare deep neural networks with traditional solution methods in quantitative economics. We conclude with a survey of neural network applications in quantitative economics and offer reasons for cautious optimism.