We present NavACL, a method of automatic curriculum learning tailored to the navigation task. NavACL is simple to train and efficiently selects relevant tasks using geometric features. In our experiments, deep reinforcement learning agents trained using NavACL significantly outperform state-of-the-art agents trained with uniform sampling -- the current standard. Furthermore, our agents can navigate through unknown cluttered indoor environments to semantically-specified targets using only RGB images. Obstacle-avoiding policies and frozen feature networks support transfer to unseen real-world environments, without any modification or retraining requirements. We evaluate our policies in simulation, and in the real world on a ground robot and a quadrotor drone. Videos of real-world results are available in the supplementary material.