The white matter structure of the human brain undergoes critical developmental milestones in utero, which we can observe noninvasively using diffusion-weighted magnetic resonance imaging. In order to understand this fascinating developmental process, we must establish the variability inherent in such a challenging imaging environment and how measurable quantities can be transformed into meaningful connectomes. We review techniques for reconstructing and studying the brain connectome and explore promising opportunities for in utero studies that could lead to more accurate measurement of structural properties and allow for more refined and insightful analyses of the fetal brain. Opportunities for more sophisticated analyses of the properties of the brain and its dynamic changes have emerged in recent years, based on the development of iterative techniques to reconstruct motion-corrupted diffusion-weighted data. Although reconstruction quality is greatly improved, the treatment of fundamental quantities like edge strength requires careful treatment because of the specific challenges of imaging in utero. There are intriguing challenges to overcome, from those in analysis due to both imaging limitations and the significant changes in structural connectivity, to further image processing to address the specific properties of the target anatomy and quantification into a developmental connectome.