The Human Connectome Project (HCP) is a collaborative 5-year effort to map human brain connections and their variability in healthy adults. A consortium of HCP investigators will study a population of 1200 healthy adults using multiple imaging modalities, along with extensive behavioral and genetic data. In this overview, we focus on diffusion MRI (dMRI) and the structural connectivity aspect of the project. We present recent advances in acquisition and processing that allow us to obtain very high-quality in-vivo MRI data, whilst enabling scanning of a very large number of subjects. These advances result from 2. years of intensive efforts in optimising many aspects of data acquisition and processing during the piloting phase of the project. The data quality and methods described here are representative of the datasets and processing pipelines that will be made freely available to the community at quarterly intervals, beginning in 2013.