Tandem-repeat (TR) domains occur in approximately one third of all proteins, yet these domains are less well understood compared with their globular counterparts. TR proteins act as molecular scaffolds that facilitate protein-protein interactions (PPIs) in diverse biological contexts. In disease pathologies such as cancers, misfolded, mutated or deregulated TR function is often the cause. However, targeting tandem-repeat proteins is challenging due to their flat and large interaction interfaces. In this thesis, I have explored the development of peptide-based inhibitors of PPIs involving two targets, Tankyrase (TNKS) the Anaphase Promoting Complex/Cyclosome (APC/C-Cdc20). TNKS belong to the poly-ADP-ribose polymerases (PARP) family of enzymes that PARylate their substrates, leading to ubiquitination and subsequent degradation. TNKS bind their protein substrates through an ankyrin-repeat domain comprising five so-called Ankyrin Repeat Clusters (ARCs). TNKS is of particular therapeutic interest in cancers due to its PARylation of Axin1, a subunit of the β-catenin destruction complex. We investigated the design of peptide inhibitors of TNKS ARC domains through a structure guided approach. We first attempted to expand the range of biophysical assays to assess ligand binding to TNKS ARCs. We then designed and tested a set of linear and chemically constrained peptides for their ability to bind to the ARCs. The APC/C is an E3 ubiquitin ligase that has broad substrate-specificity via its two WD40-domain co-activators, Cdc20 and Cdh1, which recognise three peptide motifs (degrons) on its substrates: the D-box, the KEN box and the ABBA motif. The regulation of mitotic exit is tightly controlled by modulating the levels of Cdc20 and Cdh1 through different stages of the cell cycle. Cdc20 overexpression is associated with many cancers. Currently, no specific inhibitors of the APC/C-Cdc20 exist in the clinic or in clinical trials. We designed a series of synthetic peptides based on the D-box to bind to Cdc20, and thereby modulate APC/C activity. Peptides were tested using surface plasmon resonance and differential scanning fluorimetry assays using recombinant Cdc20. Furthermore, D-box peptides were able to bind exogenous Cdc20 in mammalian cell lysates using a Cellular Thermal Shift Assay (CETSA). Lastly, I determined the co-crystal structures of three of the highest affinity D-box peptides bound to Cdc20, providing high-resolution insights into the binding interface, which should aid in the further development of Cdc20 inhibitors.