The climate change crisis requires large-scale human behaviour changes and the rapid deployment of a range of greenhouse gas emissions mitigation technologies. Among these, carbon dioxide capture and storage is an important technology that can reduce emissions from point sources. In this approach, CO2 is captured from gas emissions at industrial sources that may include power stations, hydrogen production plants, cement factories and steel factories. This is achieved using a capture material that selectively absorbs CO2 from the mixture of emitted gases (Figure ). The CO2 is then collected from the capture material via the application of heat (and/or a vacuum) and is subsequently stored in the ground where it can be permanently sequestered. A closely related technology is direct air capture, where a capture material is instead used to capture and remove carbon dioxide directly from the atmosphere. If the carbon dioxide is then collected and stored securely, this technology can offer "negative emissions", which are increasingly thought to be important in climate change mitigation pathways. A good carbon capture material for must generally have (i) large CO2 capture capacities, (ii) highly selective CO2 uptake, (iii) fast uptake kinetics, (iv) low energy consumption (joules per kg CO2 captured), and (v) long term stability to repeated cycling. The most established technology for point source carbon capture employs aqueous amine solutions to capture CO2 and is used in a number of large-scale demonstration projects. However, this technology has some limitations including relatively large energy consumption for regeneration, corrosion of the steel containers in which the amines are housed, and amine degradation (e.g. by oxidation). An active area of research is, therefore, to design new capture materials with improved performance. A large range of new carbon capture materials are under consideration, not limited to advanced amine solvents, ionic liquids and solid sorbents. In this article we focus on solid sorbents, which are generally porous materials that bind CO2 at their internal surfaces (inside their pores). A wide range of porous materials including metal-organic frameworks (MOFs), porous silicas, activated carbons and porous polymers have been explored for CO2 capture. For example, a MOF was recently reported to have excellent performance for CO2 capture via the physical adsorption of CO2 in the pores of the material. Another promising strategy is to functionalise porous materials with reactive functional groups such as amines or hydroxides. For example, amine-functionalised MOFs have shown promising performance and have enabled new adsorption mechanisms with unusual adsorption thermodynamics (see below). The design of improved carbon dioxide capture materials requires a detailed understanding of how carbon dioxide binds and moves within capture materials. Characterisation of carbon capture chemistry is often challenging and requires the use of a wide range of experimental techniques as well as simulation methods. Among these methods, nuclear magnetic resonance (NMR) spectroscopy has emerged as a powerful probe of binding chemistry and molecular dynamics. NMR experiments can be performed on liquids, solids and gases, as well as samples containing a variety of phases. In the case of solid materials, there is no requirement for crystallinity and amorphous materials can readily be studied. In this article, we review the practical considerations for carrying out NMR studies of carbon dioxide capture. We then show three case studies of how NMR methods have been developed to understand CO2 adsorption and diffusion mechanisms in MOFs.