Advanced applications of polymeric self-assembled structures require a stringent degree of control over such aspects as functionality location, morphology and size of the resulting assemblies. A loss of control in the polymeric building blocks of these assemblies can have drastic effects upon the final morphology or function of these structures. Gaining precise control over various aspects of the polymers, such as chain lengths and architecture, blocking efficiency and compositional distribution is a challenge and, hence, measuring the intrinsic mass and size dispersity within these areas is an important aspect of such control. It is of great importance that a good handle on how to improve control and accurately measure it is achieved. Additionally dispersity of the final structure can also play a large part in the suitability for a desired application. In this Tutorial Review, we aim to highlight the different aspects of dispersity that are often overlooked and the effect that a lack of control can have on both the polymer and the final assembled structure.