This report summarizes the outcomes of the NSF Workshop on Mapping and Engineering the Brain, held at Arlington, VA, during August 13-14, 2013. Three grand challenges were identified, including high spatiotemporal resolution neuroimaging, perturbation-based neuroimaging, and neuroimaging in naturalistic environments. It was highlighted that each grand challenge requires groundbreaking discoveries, enabling technologies, appropriate knowledge transfer, and multi- and transdisciplinary education and training for success.