Quadruped robots are proliferating in industrial environments where they carry sensor payloads and serve as autonomous inspection platforms. Despite the advantages of legged robots over their wheeled counterparts on rough and uneven terrain, they are still unable to reliably negotiate a ubiquitous feature of industrial infrastructure: ladders. Inability to traverse ladders prevents quadrupeds from inspecting dangerous locations, puts humans in harm's way, and reduces industrial site productivity. In this paper, we learn quadrupedal ladder climbing via a reinforcement learning-based control policy and a complementary hooked end effector. We evaluate the robustness in simulation across different ladder inclinations, rung geometries, and inter-rung spacings. On hardware, we demonstrate zero-shot transfer with an overall 90% success rate at ladder angles ranging from 70° to 90°, consistent climbing performance during unmodeled perturbations, and climbing speeds 232x faster than the state of the art. This work expands the scope of industrial quadruped robot applications beyond inspection on nominal terrains to challenging infrastructural features in the environment, highlighting synergies between robot morphology and control policy when performing complex skills. More information can be found at the project website: https://sites.google.com/leggedrobotics.com/climbingladders.