This paper presents a review of the development of optical fibers made of multiple materials, particularly including silica glass, soft glass, polymers, hydrogels, biomaterials, Polydimethylsiloxane (PDMS), and Polyperfluoro-Butenylvinyleth (CYTOP). The properties of the materials are discussed according to their various applications. Typical fabrication techniques for specialty optical fibers based on these materials are introduced, which are mainly focused on extrusion, drilling, and stacking methods depending on the materials’ thermal properties. Microstructures render multiple functions of optical fibers and bring more flexibility in fiber design and device fabrication. In particular, micro-structured optical fibers made from different types of materials are reviewed. The sensing capability of optical fibers enables smart monitoring. Widely used techniques to develop fiber sensors, i.e., fiber Bragg grating and interferometry, are discussed in terms of sensing principles and fabrication methods. Lastly, sensing applications in oil/gas, optofluidics, and particularly healthcare monitoring using specialty optical fibers are demonstrated. In comparison with conventional silica-glass single-mode fiber, state-of-the-art specialty optical fibers provide promising prospects in sensing applications due to flexible choices in materials and microstructures.