The ability to integrate complex electronic and optoelectronic functionalities within soft and thin fibers is one of today's key advanced manufacturing challenges. Multifunctional and connected fiber devices will be at the heart of the development of smart textiles and wearable devices. These devices also offer novel opportunities for surgical probes and tools, robotics and prostheses, communication systems, and portable energy harvesters. Among the various fiber-processing methods, the preform-to-fiber thermal drawing technique is a very promising process that is used to fabricate multimaterial fibers with complex architectures at micro- and nanoscale feature sizes. Recently, a series of scientific and technological breakthroughs have significantly advanced the field of multimaterial fibers, allowing a wider range of functionalities, better performance, and novel applications. Here, these breakthroughs, in the fundamental understanding of the fluid dynamics, rheology, and tailoring of materials microstructures at play in the thermal drawing process, are presented and critically discussed. The impact of these advances on the research landscape in this field and how they offer significant new opportunities for this rapidly growing scientific and technological platform are also discussed.