Our knowledge of muscle anatomy and physiology in vertebrates has increased dramatically over the last two-hundred years. Today, much is understood about how muscles contract and about the functional meaning of muscular variation at multiple scales. Progress in muscle anatomy has profited from the availability of broad comparative samples, advances in microscopy have permitted comparisons at increasingly finer scales, and progress in muscle physiology has profited from many carefully designed and executed experiments. Several avenues of future work are promising. In particular, muscle ontogeny (growth and development) is poorly understood for many vertebrate groups. We consider which types of advances in muscle functional morphology are of use to paleobiologists. These are only a modest subset for muscle anatomy and a very small subset for muscle physiology. The relationship between muscle and bone – spatially and mechanically—is critical to any future advances in “paleomyology”. Anat Rec, 301:538–555, 2018.