Imaging through opaque scattering media is critically important in applications ranging from biological and astronomical imaging to metrology and security. While the random process of scattering in turbid media produces scattered light that appears uninformative to the human eye, a wealth of information is contained in the signal and can be recovered using computational post-processing techniques. Recent studies have shown that statistical correlations present in the scattered light, known as 'memory effects', allow for diffraction-limited imaging through opaque media without detailed knowledge of (or access to) the source or scatterer. However, previous methods require that the object and/or scatterer be static during the measurement. We overcome this limitation by combining traditional memory effect imaging with coded-aperture-based computational imaging techniques, which enables us to realize for the first time single-shot video of arbitrary dynamic scenes through dynamic, opaque media. This has important implications for a wide range of real-world imaging scenarios.