Embryonic morphogenesis occurs along three orthogonal axes. While the patterning of the anterior-posterior and dorsal-ventral axes has been increasingly well characterized, the left-right (LR) axis has only recently begun to be understood at the molecular level. The mechanisms which ensure invariant LR asymmetry of the heart, viscera, and brain represent a thread connecting biomolecular chirality to human cognition, along the way involving fundamental aspects of cell biology, biophysics, and evolutionary biology. An understanding of LR asymmetry is important not only for basic science, but also for the biomedicine of a wide range of birth defects and human genetic syndromes. This review summarizes the current knowledge regarding LR patterning in a number of vertebrate and invertebrate species, discusses several poorly understood but important phenomena, and highlights some important open questions about the evolutionary origin and conservation of mechanisms underlying embryonic asymmetry.