We propose a novel supervised machine learning strategy, inspired by human learning, that enables an Agent to learn continually over its lifetime. A natural consequence is that the Agent must be able to handle an input whose label is delayed until a later time, or may not arrive at all. Our Agent learns in two steps: a short Seeding phase, in which the Agent's model is initialized with labelled inputs, and an indefinitely long Growing phase, in which the Agent refines and assesses its model if the label is given for an input, but stores the input in a finite-length queue if the label is missing. Queued items are matched against future input-label pairs that arrive, and the model is then updated. Our strategy also allows for the delayed feedback to take a different form. For example, in an image captioning task, the feedback could be a semantic segmentation rather than a textual caption. We show with many experiments that our strategy enables an Agent to learn flexibly and efficiently.