The field of left-right (LR) patterning--the study of molecular mechanisms that yield directed morphological asymmetries in otherwise symmetrical organisms--is in disarray. On one hand is the undeniably elegant hypothesis that rotary beating of inclined cilia is the primary symmetry-breaking step: they create an asymmetric extracellular flow across the embryonic midline. On the other hand lurk many early symmetry-breaking steps that, even in some vertebrates, precede the onset of ciliary flow. We highlight an intracellular model of LR patterning where gene expression is initiated by physiological asymmetries that arise from subcellular asymmetries (e.g. motor-protein function along oriented cytoskeletal tracks). A survey of symmetry breaking in eukaryotes ranging from protists to vertebrates suggests that intracellular cytoskeletal elements are ancient and primary LR cues. Evolutionarily, quirky effectors like ciliary motion were likely added later in vertebrates. In some species (like mice), developmentally earlier cues may have been abandoned entirely. Late-developing asymmetries pose a challenge to the intracellular model, but early mid-plane determination in many groups increases its plausibility. Multiple experimental tests are possible.