miRNA biogenesis is initiated upon cleavage of a primary miRNA (pri-miRNA) hairpin by Microprocessor (MP), composed of the Drosha RNase III enzyme and its partner DGCR8. Multiple pri-miRNA sequence motifs affect MP recognition, fidelity, and efficiency. Here, we performed cryo-EM and biochemical studies of several let-7 family pri-miRNAs in complex with human MP. We show that MP has structural plasticity to accommodate different pri-miRNAs. These also revealed key structural features of the 5' UG sequence motif, more comprehensively represented as the "fUN" motif. Our analysis explains how the bulged nucleotide in class-II pri-let-7 members alters Drosha cleavage, generating a noncanonical precursor with 1-nt 3' overhang. Finally, the MP-SRSF3-pri-let-7f1 structure reveals how SRSF3 interacts with the CNNC motif and Drosha's PAZ-like domain, to promote proper Drosha loading onto the basal hairpin junction. Overall, our work illuminates the mechanisms for flexible recognition, accurate cleavage, and regulated processing of different pri-miRNAs by MP.