Wave-based imaging techniques play a critical role in diverse scientific, medical, and indus- trial endeavors, from discovering hidden structures beneath the Earth’s surface to ultrasound diagnostics. They rely on accurate solutions to the forward and inverse problems for par- tial differential equations (PDEs) that govern wave propagation. Surrogate PDE solvers based on machine learning emerged as an effective approach to computing the solutions more efficiently than via classical numerical schemes. However, existing datasets for PDE surrogates offer only limited coverage of the wave propagation phenomenon. In this paper, we present WaveBench, a comprehensive collection of benchmark datasets for wave prop- agation PDEs. WaveBench (1) contains 24 datasets that cover a wide range of forward and inverse problems for time-harmonic and time-varying wave phenomena in 2D; (2) in- cludes a user-friendly PyTorch environment for comparing learning-based methods; and (3) comprises reference performance and model checkpoints of popular PDE surrogates such as U-Nets and Fourier neural operators. Our evaluation on WaveBench demonstrates the impressive performance of PDE surrogates on in-distribution samples, while simultaneously unveiling their limitations on out-of-distribution (OOD) samples. This OOD-generalization limitation is noteworthy, especially since we use stylized wavespeeds and provide abundant training data to PDE surrogates. We anticipate that WaveBench will stimulate the devel- opment of accurate wave-based imaging techniques through machine learning.