In recent years, there have a raising interest on learning under algorithmic triage, a new learning paradigm which seeks the development of machine learning models that operate under different automation levels---models that take decisions for a given fraction of instances and leave the remaining ones to human experts. However, the interplay between the prediction accuracy of the models and the human experts under algorithmic triage is not well understood. In this talk, we will start by formally characterizing under which circumstances a predictive model may benefit from algorithmic triage. In doing so, we will also demonstrate that models trained for full automation may be suboptimal under triage. Then, given any model and desired level of triage, we will show that the optimal triage policy is a deterministic threshold rule in which triage decisions are derived deterministically by thresholding the difference between the model and human errors on a per-instance level. Building upon these results, we will introduce a practical gradient-based algorithm that is guaranteed to find a sequence of triage policies and predictive models of increasing performance. Finally, we will use real data from two important applications, content moderation and scientific discovery, to illustrate our theoretical results and show that the models and triage policies provided by our gradient-based algorithm outperform those provided by several competitive baselines.