Scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM) are powerful and versatile techniques for materials science research. The technologies of beam control, aberration correction, signal collection, and data processing have all improved in recent years, leading to a move away from the acquisition single-variable images. Instead it is increasingly common, in the field of analytical S(T)EM, for whole energy spectra to be collected for post-facto compositional analysis.

The development of scanning precession electron diffraction (SPED) has enabled the rise of post-facto crystallographic investigation, but the associated analysis techniques remain relatively undeveloped. This research presents several novel applications of the family of computational methods known as multivariate statistics to SPED and SEM data.

Two methods - linear decomposition and data clustering - are investigated in detail using model, simulated, and experimental SPED data. The investigation focuses on the practical aspects of analysis - the microstructural information that can be extracted, and the artefacts that can be produced. In particular, it is demonstrated that linear decomposition produces a representation of the data that can be linked directly to microstructure, and analysed using data clustering.

Using these methods, the ``cloudy zone'', a complex two-phase microstructure present in iron-nickel meteorites, is investigated, resulting in the first direct observation of the crystallography of one of the phases, and providing a preliminary indication of the relationship between crystal structure and magnetic state of this material.

Shifting focus to SEM data, density-based clustering is applied - for the first time - to indexed electron back-scatter diffraction (EBSD) orientation data, and shown to be an ideal algorithm. The novel use of data clustering in the context of misorientation data is also presented, opening up the possibility for semi-automated crystallographic habit determination.

Finally, the application of multivariate analysis to combined EDS and EBSD data is investigated to assess the potential for quantifiable correlated structural and compositional analysis.