Plant vascular cells are joined end to end along uninterrupted lines to connect shoot organs with roots; vascular strands are thus polar, continuous, and internally aligned. What controls the formation of vascular strands with these properties? The “auxin canalization hypothesis”—based on positive feedback between auxin flow through a cell and the cell's capacity for auxin transport—predicts the selection of continuous files of cells that transport auxin polarly, thus accounting for the polarity and continuity of vascular strands. By contrast, polar, continuous auxin transport—though required—is insufficient to promote internal alignment of vascular strands, implicating additional factors. The auxin canalization hypothesis was derived from the response of mature tissue to auxin application but is consistent with molecular and cellular events in embryo axis formation and shoot organ development. Objections to the hypothesis have been raised based on vascular organizations in callus tissue and shoot organs but seem unsupported by available evidence. Other objections call instead for further research; yet the inductive and orienting influence of auxin on continuous vascular differentiation remains unique.