We often think about regeneration in terms of replacing missing structures, such as organs or tissues, with new structures generated via cell proliferation and differentiation. But at a smaller scale, single cells, themselves, are capable of regenerating when part of the cell has been removed. A classic model organism that facilitates the study of cellular regeneration in the giant ciliate Stentor coeruleus. These cells, which can grow to more than a millimeter in size, have the ability to survive after extensive wounding of their surface, and are able to regenerate missing structures. Even a small piece of a cell can regenerate a whole cell with normal geometry, in a matter of hours. Such regeneration requires cells to be able to trigger organelle biogenesis in response to loss of structures. But subcellular regeneration also relies on intracellular mechanisms to create and maintain global patterning within the cell. These mechanisms are not understood, but at a conceptual level they involve processes that resemble those seen in animal development and regeneration. Here we discuss single-celled regeneration in Stentor from the viewpoint of standard regeneration paradigms in animals. For example, there is evidence that regeneration of the oral apparatus in Stentor follows a sender-receiver model similar to crustacean eyestalk regeneration. By drawing these analogies, we find that many of the concepts already known from the study of animal-scale regeneration and development can be applied to the study of regeneration at the cellular level, such as the concepts of determination, induction, mosaic vs. regulative development, and epimorphosis vs. morphallaxis. We propose that the similarities may go beyond analogy, and that some aspects of animal development and regeneration may have evolved by exploiting pre-existing subcellular developmental strategies from unicellular ancestors.