We report the first, to the best of our knowledge, hand-in-hand collaboration between human rights activists and machine learners, leveraging crowd-sourcing to study online abuse against women on Twitter. On a technical front, we carefully curate an unbiased yet low-variance dataset of labeled tweets, analyze it to account for the variability of abuse perception, and establish baselines, preparing it for release to community research efforts. On a social impact front, this study provides the technical backbone for a media campaign aimed at raising public and deciders' awareness and elevating the standards expected from social media companies.