Polymeric micro- and nanoparticles are becoming a mainstay in biomedicine, medical diagnostics, and therapeutics, where they are used in implementing sensing mechanisms, as imaging contrast agents, and in drug delivery. Current approaches to the fabrication of such particles are typically finely tuned to specific monomer or polymer species, size ranges, and structures. We present a general scalable methodology for fabricating uniformly sized spherical polymeric particles from a wide range of polymers produced with complex internal architectures and continuously tunable diameters extending from the millimeter scale down to 50 nm. Controllable access to such a wide range of sizes enables broad applications in cancer treatment, immunology, and vaccines. Our approach harnesses thermally induced, predictable fluid instabilities in composite core/cladding polymer fibers drawn from a macroscopic scaled-up model called a "preform." Through a stack-and-draw process, we produce fibers containing a multiplicity of identical cylindrical cores made of the polymers of choice embedded in a polymer cladding. The instability leads to the breakup of the initially intact cores, independent of the polymer chemistry, into necklaces of spherical particles held in isolation within the cladding matrix along the entire fiber length. We demonstrate here surface functionalization of the extracted particles for biodetection through specific protein-protein interactions, volumetric encapsulation of a biomaterial in spherical polymeric shells, and the combination of both surface and volumetric functionalities in the same particle. These particles used in distinct modalities may be produced from the desired biocompatible polymer by changing only the geometry of the macroscopic preform from which the fiber is drawn.