Acts as catalytic component of the CCR4-NOT core complex, which in the nucleus seems to be a general transcription factor, and in the cytoplasm the major mRNA deadenylase involved in mRNA turnover (By similarity). Ccr4 has 3'-5' RNase activity with a strong preference for polyadenylated substrates and also low exonuclease activity towards single-stranded DNA (By similarity). Participates in the shortening of poly(A)-tails (PubMed:26942678). Erh1-mmi1 complex-mediated recruitment of CCR4-NOT to target RNAs promotes heterochromatin formation at RNAi-dependent heterochromatin domains (HOODs), including a subset of meiotic genes, lncRNAs and retrotransposons (PubMed:26942678). Recruitment of the CCR4-NOT complex to rDNA promotes rDNA heterochromatin assembly (PubMed:26942678). Exonucleolytic cleavage of poly(A) to 5'-AMP. Subunit of the CCR4-NOT core complex (By similarity). Interacts with pir2 (PubMed:26942678). Decreases heterochromatin formation at rDNA and subtelomeres. Belongs to the CCR4/nocturin family.