It is increasingly apparent that many important classes of molecular framework material exhibit a variety of interesting and useful types of structural disorder. This tutorial review summarises a number of recent efforts to understand better both the complex microscopic nature of this disorder and also how it might be implicated in useful functionalities of these materials. We draw on a number of topical examples including topologically-disordered zeolitic imidazolate frameworks (ZIFs), porous aromatic frameworks (PAFs), the phenomena of temperature-, pressure- and desorption-induced amorphisation, partial interpenetration, ferroelectric transition-metal formates, negative thermal expansion in cyanide frameworks, and the mechanics and processing of layered frameworks. We outline the various uses of pair distribution function (PDF) analysis, dielectric spectroscopy, peak-shape analysis of powder diffraction data and single-crystal diffuse scattering measurements as means of characterising disorder in these systems, and we suggest a number of opportunities for future research in the field.