Performing RNAi screens for factors that restrict several RNA viruses in fruit flies, Molleston et al. discovered that depletion of the 3′ to 5′ exonucleases dRrp6 or dDis3, which are the catalytic subunits of the RNA exosome complex, or depletion of dMtr4 or dZcchc7, which are subunits of the exosome RNA-binding co-factor TRAMP complex, greatly increased the levels of viral RNA in cells and in the fat body tissue. This was recapitulated upon depletion of RRP6, DIS3, MTR4 or ZCCHC7 in the virus-permissive human U2OS cells. In these cells, MTR4 and ZCCHC7 were exported from the nucleus to the cytoplasm following infection by the nuclear export protein CRM1, where they interacted with RRP6. Viral mRNAs were then selectively bound by ZCCHC7 and degraded at their 3′ ends in an exosome-dependent and ZCCHC7-dependent manner.