Efficient and precise genome editing is crucial for realizing the full research and therapeutic potential of human induced pluripotent stem cells (iPSCs). Engineered nucleases including CRISPR/Cas9 and transcription activator like effector nucleases (TALENs) provide powerful tools for enhancing gene-targeting efficiency. In this study, we investigated the relative efficiencies of CRISPR/Cas9 and TALENs in human iPSC lines for inducing both homologous donor-based precise genome editing and nonhomologous end joining (NHEJ)-mediated gene disruption. Significantly higher frequencies of NHEJ-mediated insertions/deletions were detected at several endogenous loci using CRISPR/Cas9 than using TALENs, especially at nonexpressed targets in iPSCs. In contrast, comparable efficiencies of inducing homologous donor-based genome editing were observed at disease-associated loci in iPSCs. In addition, we investigated the specificity of guide RNAs used in the CRISPR/Cas9 system in targeting disease-associated point mutations in patient-specific iPSCs. Using myeloproliferative neoplasm patient-derived iPSCs that carry an acquired JAK2-V617F point mutation and α1-antitrypsin (AAT) deficiency patient-derived iPSCs that carry an inherited Z-AAT point mutation, we demonstrate that Cas9 can specifically target either the mutant or the wild-type allele with little disruption at the other allele differing by a single nucleotide. Overall, our results demonstrate the advantages of the CRISPR/Cas9 system in allele-specific genome targeting and in NHEJ-mediated gene disruption.