With the rise of computer algorithms in administrative decision-making, concerns are voiced about their lack of transparency and discretionary space for human decision-makers. However, calls to ‘keep humans in the loop’ may be moot points if we fail to understand how algorithms impact human decision-making and how algorithmic design impacts the practical possibilities for transparency and human discretion. Through a review of recent academic literature, three algorithmic design variables that determine the preconditions for human transparency and discretion and four main sources of variation in ‘human-algorithm interaction’ are identified. The article makes two contributions. First, the existing evidence is analysed and organized to demonstrate that, by working upon behavioural mechanisms of decision-making, the agency of algorithms extends beyond their computer code and can profoundly impact human behaviour and decision-making. Second, a research agenda for studying how computer algorithms affect administrative decision-making is proposed.