Sodium-ion batteries are seen as an increasingly attractive option for large-scale energy storage, the rising price, and limited availability of lithium being seen as a major challenge for the future of the dominant lithium systems. One of the major bottlenecks for the commercialisation of sodium-ion technology is to find a suitable anode material. This search is hampered owing to major gaps in our understanding of how these systems work. The major objective of this thesis is to gain a better understanding of the mechanisms by which sodium inserts into different anode materials.Two systems are studied: hard carbons are widely viewed as the most promising anode material in the near future, yet the sodium insertion mechanism is still widely debated. Secondly, tin represents one of the highest capacity anode materials, able to achieve a 847 mAhg$^-1$, with numerous electrochemical features suggesting an interesting (dis)charge mechanism. It has previously been shown that both of these systems proceed through disordered phases, and as such, we focus on pair distribution function analysis (PDF) and solid-state NMR as local structure probes for our structural characterisation. Furthermore, to avoid relaxation effects in metastable intermediates, much of this work uses \operando methods.We present evidence from \operando $^23$Na NMR that sodium inserts into hard carbon in a two-stage mechanism: the first stage is consistent with charge localisation; after which the ions become progressively more metallic. We further investigate the structure of the pristine carbon, using PDF to demonstrate that the graphene-like fragments exhibit significant curvature. This work is then extended to a number of different carbons, both commercially made and synthesised from glucose. We present a novel method to fit PDF data for the pristine materials: using curved aperiodic, stacked graphene layers to generate the simplest model (fewest number of atoms) that explains all features of the data. \Operando measurements are presented that demonstrate expansion of the shortest C--C bonds during the first electrochemical process, along with the formation of sodium nano-clusters during the second.We then apply this novel multi-modal approach to tin anodes. We find that sodium insertion begins by conversion into NaSn$_2$, a phase consisting of stanene layers separated by sodium ions. This is then broken down into an amorphous phase, where reverse Monte Carlo refinements show that the predominant tin connectivity is chains. Further reaction with sodium results in structures containing Sn−-Sn dumbbells, which interconvert through a solid-solution mechanism. Finally, we show that Na$_{15}$Sn$_4$, can store additional sodium atoms as an off-stoichiometry compound (Na$_{15+x}$Sn$_4$). The sodium removal (charge) process is shown to begin by forming Sn--Sn dumbbells in a structure similar to the discharge phase, but with a lower sodium content (Na$_2$Sn). Following this, the structure loses all long-range order. We show, through refinements of suitable models against \operando PDF data, that the dumbbells are retained, but later transform into a second amorphous phase consisting of tin tetrahedra. Finally, we show that $\beta$-tin reforms, with no intermediate analogous to NaSn$_2$. We additionally demonstrate a substantial degree of kinetic control in these (de)alloying
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