The mechanisms behind fate specification are of great interest to developmental biologists. By understanding how organs form and take shape in the developing embryos, we can better understand how mutations and environmental factors impact congenital birth defects. Patients with Holt Oram Syndrome (HOS) carry a mutation in TBX5 and exhibit forelimb and cardiac septal defects. Often, the forelimb defects are more severe in the left arm than the right. Also, considering that the septum primum is a left-sided structure in the developing heart, the role of TBX5 in left-right patterning is particularly important. tbx5a is expressed in the anterior lateral plate mesoderm (ALPM) in zebrafish, which consists of several precursor fates: cardiac mesoderm; the pericardial sac; pharyngeal arches; and the peritoneum. At 18 hours post fertilization (hpf), the cells of the lateral ALPM undergo migration anteriorly and laterally. Both homozygous mutation in tbx5a and Tbx5a deficiency result in forelimb and heart looping defects, similar to patients of HOS. Studying the process of fate specification and function of tbx5a in the ALPM of zebrafish was the goal of my dissertation. I elucidate a single-cell resolution fate map of the lateral ALPM at 18 hpf. I demonstrate that the ALPM is not organized into segregated fate regions but gives rise to precursors of intermingled fates. I discover an asymmetrical contribution of lateral ALPM-derived heart precursors–specifically that twice as many heart precursors arise from the right side as from the left side. I present cell tracking analyses and regional-to-large-scale labeling of the lateral ALPM and find similar left/right asymmetries in migration dynamics and contributions to the larval heart. These findings corroborate the differences found in the fate map and show that the observed asymmetries are dependent upon Tbx5a expression. These data implicate tbx5a function in establishing and maintaining cardiac left/right asymmetry and cell specification. The work in this dissertation expands upon the current knowledge of organ specification in zebrafish and how tbx5a functions in the development of the heart, pericardial sac, pharyngeal arches, and peritoneum. In conclusion, my work culminates in proposing models of progressive specification of the ALPM and of tbx5a function that differs across time and precursor fates.