Microstructured optical fiber-based sensors (MOF) have been widely developed finding numerous applications in various fields of photonics, biotechnology, and medicine. High sensitivity to the refractive index variation, arising from the strong interaction between a guided mode and an analyte in the test, makes MOF-based sensors ideal candidates for chemical and biochemical analysis of solutions with small volume and low concentration. Here, we review the modern techniques used for the modification of the fiber’s structure, which leads to an enhanced detection sensitivity, as well as the surface functionalization processes used for selective adsorption of target molecules. Novel functionalized MOF-based devices possessing these unique properties, emphasize the potential applications for fiber optics in the field of modern biophotonics, such as remote sensing, thermography, refractometric measurements of biological liquids, detection of cancer proteins, and concentration analysis. In this work, we discuss the approaches used for the functionalization of MOFs, with a focus on potential applications of the produced structures.