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. CCR4 has 3'-5' RNase activity with a strong preference for polyadenylated substrates and also low exonuclease activity towards single-stranded DNA. Discovered because of its role in the control of ADH2 gene expression. It is required for the expression of genes involved in non-fermentative growth and it mediates or is required for the action of the SPT6 and SPT10 genes. Exonucleolytic cleavage of poly(A) to 5'-AMP. Subunit of the 1.0 MDa CCR4-NOT core complex that contains CCR4, CAF1, NOT1, NOT2, NOT3, NOT4, NOT5, CAF40 and CAF130. In the complex interacts with NOT1. The core complex probably is part of a less characterized 1.9 MDa CCR4-NOT complex. The 169 C-terminal residues are important for deadenylase activity. Present with 2780 molecules/cell in log phase SD medium. Belongs to the CCR4/nocturin family.