The fiber thermal drawing process has emerged as a simple and scalable technique for the fabrication of multifunctional and flexible electronics. The integration of materials with various physical and functional properties in well-defined architectures opened a wide range of applications. However, the trend of increasing number of functionalities, which requires a reduction in size of each fiber constituent, revealed the importance of instability mechanisms that need to be better understood and overcome. In this thesis, we address several challenges associated with the process-microstructure relationship that govern the achievable feature sizes. We first tackle the problem of thermal reflow of polymeric textures induced by the Laplace pressure. We develop a reflow model that can be applied to periodic textures during isothermal annealing and extend it to the thermal drawing process. After validating our model with experimental data, we show that the reflow driving force can be significantly reduced by codrawing two materials of low interfacial tension. We demonstrate this finding by drawing sub-100 nm textures on polycarbonate fibers. The second part focuses on the influence of the drawing parameters on the degree of polymer chain alignment which induces serious shrinkage upon heating. We reveal that the drawing stress, which depends on the drawing speed and temperature, controls the shrinkage stress. Furthermore, we show that the degree of chain orientation increases linearly with the stress at low thermal drawing stress, and then saturates, which correlates well with the amount of shrinkage observed. We then highlight the use of this process-dependent alignment to tune the mechanical properties of the fibers and the bending behavior of multi-material fibers. Finally, a heat treatment is proposed for reducing the chain alignment to increase the dimensional stability of fiber devices such as temperature sensors. In the third part, we switch our attention to inorganic materials and discuss the long-lasting challenge of the thermal drawing of bulk metallic glasses (BMGs) which enables us to circumvent the size limitation of crystalline metal electrodes due to capillary instabilities. We first demonstrate the production of well-ordered Pt57.5Cu14.7Ni5.3P22.5 (Pt-MG) ribbons within a polyetherimide matrix with uniform features down to 40 nm. We reveal via transmission electron microscopy analyses a crystallization-induced break up. Furthermore, our approach enables us to study the influence the process on the crystallization kinetics of the Pt-MG ribbons. We show that the latter is enhanced by the increase in deformation and decrease in size both at the micro- and nanoscale. We then demonstrate the ability of thermal drawing of another BMG, Au49Ag5.5Pd2.3Cu26.9Si16.3, by selecting a poly(methylmetacrylate) cladding with matching thermo-mechanical and rheological properties. The ultimate feature size, caused by the onset of crystallization, is a few hundred nanometers. Finally, we show two examples of devices highlighting the novel functionalities enabled by the thermal drawing of BMGs. We produce and test in vivo, in collaboration with colleagues in the bio-engineering department, neural probes allowing electrical stimulation, recording and precise drug delivery, and electrochemical sensors integrating the three-electrode system in a single fiber.