Measuring atomic-resolution images of materials with x-ray photons during chemical reactions or physical transformations resides at the technological forefront of x-ray science. New x-ray-based experimental capabilities have been closely linked with advances in x-ray sources, a trend that will continue with the impending arrival of x-ray-free electron lasers driven by electron accelerators. We discuss recent advances in ultrafast x-ray science and coherent imaging made possible by linear-accelerator-based light sources. These studies highlight the promise of ultrafast x-ray lasers, as well as the technical challenges and potential range of applications that will accompany these transformative x-ray light sources.