MicroRNAs are short non-coding RNAs that are evolutionarily conserved and are pivotal post-transcriptional mediators of gene regulation. Together with transcription factors and epigenetic regulators, they form a highly interconnected network whose building blocks can be classified depending on the number of molecular species involved and the type of interactions amongst them. Depending on their topology, these molecular circuits may carry out specific functions that years of studies have related to the processing of gene expression noise. In this review, we first present the different over-represented network motifs involving microRNAs and their specific role in implementing relevant biological functions, reviewing both theoretical and experimental studies. We then illustrate the recent advances in synthetic biology, such as the construction of artificially synthesised circuits, which provide a controlled tool to test experimentally the possible microRNA regulatory tasks and constitute a starting point for clinical applications.