This talk will focus on method developments to understand structure and dynamics in Li, Na and Mg batteries using a series of local structural probes. Recent studies to improve our understanding of hard carbons for Na-ion batteries will be discussed using both NMR and pair distribution function (PDF) analysis. Here we use both methods to correlate structure with the capacity observed in both the sloping and flat, low voltage component of the electrochemical curve. NMR studies to study dynamics in lithium-ion cathode and anode materials will be discussed. For example, a series of high rate Nb-oxide electrodes and the structures that allow high Li transport and extremely high rates even when micrometer-sized will be described. These structures adopt crystallographic shear and bronze-like structures, and retain open diffusional channels for Li over a wide range of lithium compositions. In part, this is due to structural motifs present in, for example, the shear structures that prevent rotation of the perovskite corner edge sharing octahedra that clamp the Li in place in ReO₃-type structures. Their lithium-ion diffusion coefficients (D_Li) were measured with pulsed field gradient NMR spectroscopy and have room temperature values that are several orders-of-magnitude faster than typical electrode materials.