Polynucleotide ligases preserve the integrity of the 3'-5' phosphodiester backbone in DNA and RNA -- a crucial aspect in the life cycle of any organism. This thesis explores various mechanisms that are employed during RNA damage and repair. Cyclic phosphates are key species in cellular RNA damage and repair pathways. Mechanistically, there are two distinct enzymatic routes to generate 2',3'-cyclic phosphate ends - transesterification and de novo cyclization using ATP. In this work, I have investigated reaction pathways that generate and utilize these cyclic phosphate ends in the context of RNA damage and repair. Specifically, I have studied cyclic-phosphate generation by RtcA ( E. coli Rtc homolog) and PaT (a eukaryal anticodon nuclease) from a structure-function perspective as well as cyclic-phosphate utilization by RtcB, a recently discovered RNA ligase. I trapped and crystallized E. coli RtcA at discrete stages of the reaction pathway. Crystal structures of RtcA*ATP binary complex, RtcA*ATP*metal ternary complex and an RtcA*AMP product complex were solved. These structural snapshots helped reconstruct the covalent adenylylation of RtcA at atomic resolution. The key findings from the study illustrated: i) metal induced reorganization of the phosphates of ATP to place the pyrophosphate leaving group apical to the active site histidine for an inline nucleophilic attack, ii) metal is not required for steps 2 & 3 of cyclization, later confirmed by biochemical assays, iii) molecular roles of conserved residues in the RtcA active site were assigned. I was also able to demonstrate the ligase-like capability of RtcA to adenylylate 5'-monophosphate ends of DNA and RNA. In E. coli and several other bacteria, rtcA is part of an operon with rtcB - a gene encoding for a protein whose function was unknown until 2011. RtcB was found to be a bona-fide tRNA ligase in vitro and in vivo . Using biochemical and mass spectrometric methods, I tested the veracity of the proposed d̀irect' ligation mechanism of RtcB. By isolating intermediates at discrete stages in the reaction pathway, I discovered that the 2',3'-cyclic phosphate/5'-hydroxyl ligation catalyzed by RtcB is not direct and entails - (i) reaction of His337 with GTP to form a covalent RtcB-(histidinyl-N)-GMP intermediate; (ii) hydrolysis of the 2',3'-cyclic phosphate to a 3'-phosphate (iii) transfer of guanylate to a RNA 3'-phosphate to form RNAppG intermediate; (iv) attack of 5'-hydroxyl moiety on the -RNAppG end to form the sealed phosphodiester. RtcB catalyzed RNA ligation is the first known example of a polynucleotide ligase that works via 3'-end activation. It raises the possibility of an alternative enzymology based on 3'-activated ends in nucleic acids. Fungal anticodon nucleases (ACNases) are toxins that cause growth arrest of foreign species by cleaving a single phosphodiester bond in the anticodon stem loop of specific tRNAs. Any structure function analysis on ACNases has so far evaded us for two reasons: 1) these toxins are sui generis and lack similarity in primary structure to any known nucleases, 2) there are no known three dimensional structures of any eukaryal ACNase. To that end, I crystallized and solved the structure of an ACNase from Pichia acaciae at 1.8 [Angstrom] resolution. The structure of Pichia acaciae toxin (PaT) reveals a novel three-dimensional fold with unique topology. Further, using an in vivo yeast growth arrest assay and an in vitro anticodon stem-loop cleavage assay, I have been able to define the enzyme active site, and elucidate the mechanism of action of this unique class of RNA damage proteins.