Performing agile navigation with four-legged robots is a challenging task due to the highly dynamic motions, contacts with various parts of the robot, and the limited field of view of the perception sensors. In this paper, we propose a fully-learned approach to train such robots and conquer scenarios that are reminiscent of parkour challenges. The method involves training advanced locomotion skills for several types of obstacles, such as walking, jumping, climbing, and crouching, and then using a high-level policy to select and control those skills across the terrain. Thanks to our hierarchical formulation, the navigation policy is aware of the capabilities of each skill, and it will adapt its behavior depending on the scenario at hand. Additionally, a perception module is trained to reconstruct obstacles from highly occluded and noisy sensory data and endows the pipeline with scene understanding. Compared to previous attempts, our method can plan a path for challenging scenarios without expert demonstration, offline computation, a priori knowledge of the environment, or taking contacts explicitly into account. While these modules are trained from simulated data only, our real-world experiments demonstrate successful transfer on hardware, where the robot navigates and crosses consecutive challenging obstacles with speeds of up to two meters per second. The supplementary video can be found on the project website: https://sites.google.com/leggedrobotics.com/agile-navigation