Chromosomal instability (CIN) describes ongoing numerical and structural chromosomal aberrations in cancer cells, leading to intra-tumour heterogeneity and is frequently associated with polyploidy and aneuploidy. CIN is a frequent event in solid tumours and previous evidence has implicated CIN with acquired multidrug resistance, intrinsic taxane resistance and poor patient prognosis. In this thesis, I have attempted to explore mechanisms required for the initiation of CIN and the tolerance of this pattern of genome instability. Firstly, I have attempted to identify clinically relevant therapeutics that may have specific activity in CIN+ tumour cell lines. Focusing on a panel of colorectal cancer cell lines, classified as either CIN+ or CIN-, and treating them individually with kinase inhibitor and cytotoxic agent libraries, I demonstrated that CIN+ cell lines displayed significant intrinsic multidrug resistance. Next, I addressed if specific means to target CIN+ cells could be identified through pharmacological and RNA interference (RNAi) screens. No compounds were observed to be preferentially cytotoxic towards CIN+ cells in the pharmacological screen. A whole genome RNAi screen was performed to identify CIN+ specific survival pathways using isogenic cell line models of CIN. No genes were identified that conferred preferential cell death when silenced in CIN+ cells, despite sufficient statistical power to detect such targets. Using integrative genomics techniques and cell cycle data from this RNAi screen, I endeavoured to identify clinically relevant initiators of aneuploidy in colorectal cancer, that revealed both known and potential novel regulators of polyploidy. Finally, I endeavoured to identify a mechanistic basis for the taxane-sensitising phenotype associated with the silencing of the ceramide transporter, CERT, which may reveal means to target CIN+ cells. I demonstrated that CERT silencing sensitises paclitaxel-treated cells to cell death in a LAMP2-dependent manner that is associated with autophagy flux and may target death of multinucleated cells specifically.