Although vertebrates appear bilaterally symmetric on the outside, various internal organs, including the heart, are asymmetric with respect to their position and/or their orientation based on the left/right (L/R) axis. The L/R axis is determined during embryo development. Determination of the L/R axis is fundamentally different from the determination of the anterior-posterior or the dorsal-ventral axis. In all vertebrates a ciliated organ has been described that induces a left-sided gene expression program, which includes Nodal expression in the left lateral plate mesoderm. To have a better understanding of organ laterality it is important to understand how L/R patterning induces cellular responses during organogenesis. In this review, we discuss the current understanding of the mechanisms of L/R patterning during zebrafish development and focus on how this affects cardiac morphogenesis. Several recent studies have provided unprecedented insights into the intimate link between L/R signaling and the cellular responses that drive morphogenesis of this organ.