A key development in archaeology is the increasing agency of the digital tools brought to bear on archaeological practice. Roles and tasks that were previously thought to be uncomputable are beginning to be digitalized, and the presumption that computerization is best suited to well-defined and restricted tasks is starting to break down. Many of these digital devices seek to reduce routinized and repetitive work in the office environment and in the field. Others incorporate data-driven methods to represent, store, and manipulate information in order to undertake tasks previously thought to be incapable of being automated. Still others substitute the human component in environments which would be otherwise be inaccessible or dangerous. Whichever applies, separately or in combination, such technologies are typically seen as black-boxing practice with often little or no human intervention beyond the allocation of their inputs and subsequent incorporation of their outputs in analyses. This paper addresses the implications of this shift to algorithmic automated practices for archaeology and asks whether there are limits to algorithmic agency within archaeology. In doing so, it highlights several challenges related to the relationship between archaeologists and their digital devices.