The process in which double-stranded RNAs silence cognate genes. Involves posttranscriptional gene inactivation ('silencing') both of transgenes or dsRNA introduced into a germline, and of the host gene(s) homologous to the transgenes or dsRNA. This silencing is triggered by the introduction of transgenes or double-stranded RNA (dsRNA), and can occur through a specific decrease in the level of mRNA, or by negative regulation of translation, of both host genes and transgenes.