La-related proteins (LARPs) share a La motif (LaM) followed by an RNA recognition motif (RRM). Together these are termed the La-module that, in the prototypical nuclear La protein and LARP7, mediates binding to the UUU-3'OH termination motif of nascent RNA polymerase III transcripts. We briefly review La and LARP7 activities for RNA 3' end binding and protection from exonucleases before moving to the more recently uncovered poly(A)-related activities of LARP1 and LARP4. Two features shared by LARP1 and LARP4 are direct binding to poly(A) and to the cytoplasmic poly(A)-binding protein (PABP, also known as PABPC1). LARP1, LARP4 and other proteins involved in mRNA translation, deadenylation, and decay, contain PAM2 motifs with variable affinities for the MLLE domain of PABP. We discuss a model in which these PABP-interacting activities contribute to poly(A) pruning of active mRNPs. Evidence that the SARS-CoV-2 RNA virus targets PABP, LARP1, LARP 4 and LARP 4B to control mRNP activity is also briefly reviewed. Recent data suggests that LARP4 opposes deadenylation by stabilizing PABP on mRNA poly(A) tails. Other data suggest that LARP1 can protect mRNA from deadenylation. This is dependent on a PAM2 motif with unique characteristics present in its La-module. Thus, while nuclear La and LARP7 stabilize small RNAs with 3' oligo(U) from decay, LARP1 and LARP4 bind and protect mRNA 3' poly(A) tails from deadenylases through close contact with PABP.Abbreviations: 5'TOP: 5' terminal oligopyrimidine, LaM: La motif, LARP: La-related protein, LARP1: La-related protein 1, MLLE: mademoiselle, NTR: N-terminal region, PABP: cytoplasmic poly(A)-binding protein (PABPC1), Pol III: RNA polymerase III, PAM2: PABP-interacting motif 2, PB: processing body, RRM: RNA recognition motif, SG: stress granule.