The aim of this thesis is to exfoliate and characterise misfit layer chalcogenides (MLCs). There is a focus on the application of analytical scanning transmission electron microscopy (STEM), in particular viewed in cross section. The cross section specimens are prepared by focused ion beam (FIB), as such novel methods for the optimisation of this technique for preparation of specimens suitable for high quality STEM analysis are proposed. Misfit layer chalcogenides are a group of compounds formed from alternating layers of pseudo-tetragonal (T) PbS like, and pseudo-hexagonal (H) transition mental dichalcogenide like layers. They demonstrate remarkable flexibility in incorporating different elements into the layers allowing for the creation of crystals with a broad range of properties. Previously, MLCs [(PbS)][(NbS2)2] and [(SmS)][(NbS2)2] have been successfully exfoliated to single unit cell thickness. However, these compounds possess a stacking sequence (n=1, m=2, where n and m refer to the stacking sequence of T and H layers respectively) which contains a van der Waals (vdW) gap. Here we explore the exfoliation of two naturally occurring MLCs, franckeite (n=2, m=1) and cylindrite (n, m=1), which do not possess a vdW gap. The successful exfoliation of these crystals demonstrates that exfoliation is invariant to stacking sequence. As such all MLCs can be considered as realistic targets as 2D materials. Furthermore we demonstrate the power of cross sectional analytical STEM for the characterisation and analysis of MLCs, and directly observe features within the induvial layers, which are inaccessible through other characterisation techniques. Including elemental ordering and structural features previously not described in literature, which have allowed for a better understanding of the macroscopic structures of franckeite and cylindrite. Specimen preparation by FIB is optimised for cylindrite specimens, yielding a new procedure for the preparation of these samples. Finally, two novel methods for the in-situ thickness measurements of TEM lamellae prepared by FIB are proposed. The first method describes the accurate calibration of a FIB instrument, and the second allows for accurate thickness estimation without the need for prior calibration, through the use of Monte Carlo modelling. The Monte Carlo method allows for high quality lamella from new materials to be milled to a predetermined thickness with outstanding accuracy. Furthermore a workflow for the automation of TEM lamellae preparation is presented, which utilises this accurate modelling.