The human proteome includes many proteins that are entirely disordered or contain long disordered regions. Although these proteins are linked with many diseases, there are currently no clinically-approved drugs that have been shown to target these proteins in their monomeric forms. In fact, disordered proteins are generally considered to be 'untargettable'. This situation has arisen from a lack of understanding of how small molecules bind disordered proteins. In this thesis, I combine biophysical experiments and computational ensemble determination techniques (metadynamic metainference) to characterise small molecule interactions with disordered proteins. After an introduction to the field in Chapter 1, I focus on the interaction of a drug-like molecule with a peptide from an oncogenic transcription factor, c-Myc, in Chapter 2. I observed this interaction to be of entropic nature, and characterise the binding at the atomic level using simulations restrained with NMR data. The binding is extremely dynamic, such that both the small molecule and disordered protein explore many conformations in the bound state. Nevertheless, this interaction also shows signs of sequence specificity. In the remaining chapters, I generalise this approach to probe small molecule binding to the monomeric form of the amyloid β peptide (Aβ), whose aggregation is a hallmark of Alzheimer's disease. In Chapter 3, I employ metadynamic metainference restrained with NMR data to identify the structural origins Aβ42's lower solubility with respect to Aβ40, and show how this structural insight can be applied towards novel therapeutic development targeting this disordered protein. In Chapter 4, using both experimental and computational techniques, I identify and characterise a small molecule that sequesters Aβ42 in its soluble monomeric form and prevents its toxic aggregation. A detailed understanding of the binding mechanisms between small molecules and disordered proteins may lead to the ability to engineer improved binding interactions, thus yielding drugs targeting these proteins that are highly prevalent in many major human diseases including cancer, neurodegeneration, cardiovascular disease, and diabetes.