I recently proposed the lottery ticket hypothesis: that the dense neural networks we typically train have much smaller subnetworks capable of reaching full accuracy from early in training. This hypothesis raises (1) scientific questions about the nature of overparameterization in neural network optimization and (2) practical questions about our ability to accelerate training. In this talk, I will discuss established results and the latest developments in my line of work on the lottery ticket hypothesis, including the empirical evidence for these claims on small vision tasks, changes necessary to scale these ideas to practical settings, and the relationship between these subnetworks and their "stability" to the noise of stochastic gradient descent. I will also describe my vision for the future of research on this topic.