The activities and genome-wide specificities of CRISPR-Cas Cpf1 nucleases are not well defined. We show that two Cpf1 nucleases from Acidaminococcus sp. BV3L6 and Lachnospiraceae bacterium ND2006 (AsCpf1 and LbCpf1, respectively) have on-target efficiencies in human cells comparable with those of the widely used Streptococcus pyogenes Cas9 (SpCas9). We also report that four to six bases at the 3' end of the short CRISPR RNA (crRNA) used to program Cpf1 nucleases are insensitive to single base mismatches, but that many of the other bases in this region of the crRNA are highly sensitive to single or double substitutions. Using GUIDE-seq and targeted deep sequencing analyses performed with both Cpf1 nucleases, we were unable to detect off-target cleavage for more than half of 20 different crRNAs. Our results suggest that AsCpf1 and LbCpf1 are highly specific in human cells.