Models for understanding and holding systems accountable have long rested upon ideals and logics of transparency. Being able to see a system is sometimes equated with being able to know how it works and govern it — a pattern that recurs in recent work about transparency and computational systems. But can “black boxes’ ever be opened, and if so, would that ever be sufficient? In this article, the authors critically interrogate the ideal of transparency, trace some of its roots in scientific and socio-technical cultures, and present 10 limitations to its application. The authors specifically focus on the inadequacy of transparency for understanding and governing algorithmic systems and sketch an alternative typology of algorithmic accountability grounded in constructive engagements with the limitations of transparency ideals.