Over the past three decades in cellular neuroscience there has been a shift towards the view of the 'tripartite synapse', where, astrocytes -- as well as the pre-synapse and post-synapse -- are involved in synaptic signalling. The migration of astrocytes to form branched networks in the brain is, therefore, of great interest in understanding brain development and neuronal function. Migration is a complex interplay between cytoskeletal reorganisation and cell mechanical stiffness. In order to improve understanding of this process, correlative measurements of cytoskeletal organisation and mechanical stiffness are required. To investigate astrocyte migration a technique combining atomic force microscopy (AFM) with stimulated emission depletion (STED) microscopy was developed. First a custom STED microscope was developed. To facilitate the design of this system the theoretical performance of a range of STED techniques (cw-STED, time-gated STED, pulsed STED and RESOLFT) were compared, identifying that pulsed STED theoretically has the highest photon efficiency. A pulsed STED microscope, which uses adaptive optics, was then designed, developed and characterised. The microscope was found to achieve resolutions below 50 nm. The STED microscope was combined with a commercial AFM to study live cells. Using the recently developed SiR-actin and SiR-tubulin dyes and AFM probes optimised for live cell mechanical property studies, images of the actin and tubulin cytoskeleton were correlated with AFM topography and mechanical stiffness measurements. It was found that, in astrocytes, actin contributes significantly both to astrocyte stiffness and topography. Investigations of migrating cells showed differences in actin organisation and mechanical stiffness between the basis and leading edge of migration. A further study was performed, investigating the effects of the gap-junction protein connexin30, which is expressed during the early stages of brain development, on migration. This protein was found to inhibit the actin reorganisation and mechanical stiffness changes observed in basal conditions. Overall the combination of mechanosensitive AFM measurements with advanced microscopy, such as super-resolution, on live cells is a promising approach which will enable a range of investigations, for instance when studying cell structural remodeling during brain development or tumorigenesis.