C(4) photosynthesis is an adaptive trait conferring an advantage in warm and open habitats. It originated multiple times and is currently reported in 18 plant families. It has been recently shown that phosphoenolpyruvate carboxylase (PEPC), a key enzyme of the C(4) pathway, evolved through numerous independent but convergent genetic changes in grasses (Poaceae). To compare the genetics of multiple C(4) origins on a broader scale, we reconstructed the evolutionary history of the C(4) pathway in sedges (Cyperaceae), the second most species-rich C(4) family. A sedge phylogeny based on two plastome genes (rbcL and ndhF) has previously identified six fully C(4) clades. Here, a relaxed molecular clock was used to calibrate this tree and showed that the first C(4) acquisition occurred in this family between 19.6 and 10.1 Ma. According to analyses of PEPC-encoding genes (ppc), at least five distinct C(4) origins are present in sedges. Two C(4) Eleocharis species, which were unrelated in the plastid phylogeny, acquired their C(4)-specific PEPC genes from a single source, probably through reticulate evolution or a horizontal transfer event. Acquisitions of C(4) PEPC in sedges have been driven by positive selection on at least 16 codons (3.5% of the studied gene segment). These sites underwent parallel genetic changes across the five sedge C(4) origins. Five of these sites underwent identical changes also in grass and eudicot C(4) lineages, indicating that genetic convergence is most important within families but that identical genetic changes occurred even among distantly related taxa. These lines of evidence give new insights into the constraints that govern molecular evolution.