Cytokinesis, the final step in cell division, partitions the contents of a single cell into two. In animal cells, cytokinesis occurs through cortical remodeling orchestrated by the anaphase spindle. Cytokinesis relies on a tight interplay between signaling and cellular mechanics and has attracted the attention of both biologists and physicists for more than a century. In this review, we provide an overview of four topics in animal cell cytokinesis: (a) signaling between the anaphase spindle and cortex, (b) the mechanics of cortical remodeling, (c) abscission, and (d) regulation of cytokinesis by the cell cycle machinery. We report on recent progress in these areas and highlight some of the outstanding questions that these findings bring into focus.