The human genome contains more than 1,000 microRNA (miRNA) genes, which are transcribed mainly by RNA polymerase II. The canonical pathway of miRNA biogenesis includes the nuclear processing of primary transcripts (pri-miRNAs) by the ribonuclease Drosha and further cytoplasmic processing of pre-miRNAs by the ribonuclease Dicer. This review discusses the issue of miRNA end heterogeneity generated primarily by Drosha and Dicer cleavage and focuses on the structural aspects of the Dicer step of miRNA biogenesis. We examine the structures of miRNA precursors, both predicted and experimentally determined, as well as the influence of various motifs that disturb the regularity of pre-miRNA structure on Dicer cleavage specificity. We evaluate the structural determinants of the length diversity of miRNA generated by Dicer from different precursors and highlight the importance of asymmetrical motifs. Finally, we discuss the impact of Dicer protein partners on cleavage efficiency and specificity and propose the contribution of pre-miRNA structural plasticity to the dynamics of the dicing complex.