Non-syndromic orofacial clefting, including cleft lip with or without cleft palate (CL/P), and cleft palate alone (CP), is a common disorder with a strong genetic underpinning. Genome-wide association studies (GWAS) have detected common variants associated with risk for this disorder. However, GWAS only explain a portion of the overall heritability for orofacial clefting; much of the risk is conferred by unidentified rare sequence variants. It is unclear what genes harbor such variants. In addition, the mechanistic basis of risk conferred by common, risk-associated variants (i.e., identified by GWAS) is unknown. Here we present our approach to both challenges using zebrafish. Most patients with Van der Woude orofacial clefting syndrome have mutations in IRF6, encoding Interferon Regulatory Factor 6, an essential member of the gene regulatory network (GRN) governing differentiation of periderm. Genes encoding other members of this GRN are candidates to harbor rare variants that confer risk for orofacial clefting. With epistasis experiments, we found that Krüppel-like factor 17 (Klf17) and Grainyhead-like 3 (Grhl3) both act downstream of Irf6 in the zebrafish periderm GRN. Klf17 expression is absent from mammalian oral epithelium, but a close homologue, Klf4, is expressed in this tissue and is required for the differentiation of epidermis. Chromosome configuration capture and reporter assays indicate that IRF6 directly regulates an oral-epithelium enhancer of KLF4. Next, we sequenced KLF4 in approximately non-syndromic CL/ P cases and controls. Two patient-derived KLF4 variants disrupted periderm differentiation upon forced expression in zebrafish embryos. Thus, rare variants of KLF4 account for some of the missing heritability for non-syndromic CL/P. Further, we detected rare coding variants of GRHL3 in some patients with Van der Woude syndrome, and found they disrupted periderm differentiation in zebrafish, explaining some of the missing heritability for this disorder. Finally, a recent GWAS revealed that a common coding variant of GRHL3 is associated with risk for non-syndromic CP. This variant, but not other common coding variants of GRHL3, has dominant negative activity in zebrafish. In sum, functional studies in zebrafish helped identify rare variants that contribute to the missing heritability for syndromic and non-syndromic forms of CL/P, and identified the mechanistic basis of a common variant associated with risk for non-syndromic CP.