The exosome plays major roles in RNA processing and surveillance but the in vivo target range and substrate acquisition mechanisms remain unclear. Here we apply in vivo RNA crosslinking (CRAC) to the nucleases (Rrp44, Rrp6), two structural subunits (Rrp41, Csl4) and a cofactor (Trf4) of the yeast exosome. Analysis of wild-type Rrp44 and catalytic mutants showed that both the CUT and SUT classes of non-coding RNA, snoRNAs and, most prominently, pre-tRNAs and other Pol III transcripts are targeted for oligoadenylation and exosome degradation. Unspliced pre-mRNAs were also identified as targets for Rrp44 and Rrp6. CRAC performed using cleavable proteins (split-CRAC) revealed that Rrp44 endonuclease and exonuclease activities cooperate on most substrates. Mapping oligoadenylated reads suggests that the endonuclease activity may release stalled exosome substrates. Rrp6 was preferentially associated with structured targets, which frequently did not associate with the core exosome indicating that substrates follow multiple pathways to the nucleases.