Battery technologies are of fundamental importance to the modern world and the current development of electric vehicles, as well as grid storage of renewable energy, is placing an increased demand on Li-ion batteries (LIBs). Na-ion batteries (NIBs) are seen as a promising alternative to LIBs due to their lower cost and environmental impact. As Na has a similar chemistry to Li, the transfer of battery technology is also expected to be straightforward, but this is not always the case. For example, graphite is the most common anode for LIBs; however, it is not able to accommodate Na under normal circumstances. Disordered hard carbons are often used instead, this is despite their structure and sodiation mechanism not being fully understood. The choice of electrolyte for a battery is critical and if certain electrolyte solvents such as diglyme are used, co-intercalation of Na into graphite occurs. In Chapter 3, the interactions between diglyme molecules and graphite are investigated using various techniques, including nuclear magnetic resonance spectroscopy and thermogravimetric analysis. Similar techniques were then also used to provide evidence that diglyme also co-intercalates into the disordered hard carbons that are normally used as anodes, albeit to a lesser extent than in graphite. Chapter 4 sets out to probe the dynamics of diglyme co-intercalated into hard carbon using 2H NMR and simulations, and then use the dynamics of diglyme as an indirect probe for the structure of hard carbon. It was found that the motion of diglyme can be described by simulating a molecular rotation of diglyme with a lognormal distribution of rotation rates, which is indicative of the range of different sites that Na-diglyme complexes can occupy in hard carbon. By probing hard carbon at different states of charge, it was also found that the motion of diglyme increased on sodiation, indicating that hard carbon expands as Na intercalates into the structure, giving diglyme more space to move in. By comparing hard carbons with different capacities, it was also found that as capacity increases, the motion of diglyme decreases, possibly reflecting the increasingly graphitic nature of high-capacity hard carbons. Within a NIB, the surface layer that forms on the anode during cycling, i.e., the solid electrolyte interphase (SEI), is of crucial importance to the performance of the battery as it inhibits the transfer of electrons whilst also allowing the desired Na+ ions to pass through. Despite this, the structure and composition of the SEI in NIBs is not fully characterised. There have been several works that aim to study the SEI formed on hard carbon; however, these reports study hard carbons cycled in half-cells where Na metal is used as a counter electrode. Commercial NIBs would be full-cells that use high voltage cathodes, such as transition metal oxides, and it is likely that that the SEI formed in half-cells will be heavily influenced by Na metal as it is a strong reducing agent. Therefore, in Chapter 5 we study the SEI formed on hard carbon anodes in full- and half-cells compared using a combination of NMR and X-ray photoelectron spectroscopy (XPS). For half-cells, it was found that SEI forms more quickly than full-cells, even before any cycling has taken place. Furthermore, whilst all SEIs were composed of species such as NaF, Na alkyl carbonates and NaPO2F2, half-cells had an increased amount of polymeric species in their SEIs compared to the full cells.