Methods and constructs for the multiplex expression of highly active CRISPR guide RNAs (gRNAs) from RNA Polymerase II and III promoters, optionally in mammalian cells. The present invention is based, at least in part, on the discovery that Csy4, an endoribonuclease that recognizes a short RNA hairpin sequence, can be used to cleave out multiple functional gRNAs encoded on a single longer RNA transcript (produced from an RNA pol II or III promoter) in which the individual gRNAs are separated by Csy4 cleavage sites.