Integration of piezoelectric materials in composite and textile structures is promising to create smart textiles with sensing or energy harvesting functionalities. The most direct integration that combines wearability, comfort and piezoelectric efficiency consists in using fibers made of piezoelectric materials. The latter include inorganic ceramics or organic polymers. Ceramics have outstanding piezoelectric properties but can not be easily melted or solubilized in a solvent to be processed in the form of fibers. They have to be spun from precursor materials and thermally treated afterwards for densification and sintering. These delicate processes have to be carefully controlled to optimize the piezoelectric properties of the fibers. On the other hand, organic piezoelectric polymers, such as Polyvinylidene fluoride (PVDF), can be spun by more 2 conventional textile fibers technologies. In addition to enjoy an easier manufacturing, organic piezoelectric fibers display flexibility that facilitates their integration and use in smart textiles. However, organic fibers suffer from a low piezoelectric efficiency. This article reviews the processing techniques and their specific limitations and advantages to realize single component or coaxial piezofibers. Fundamental challenges related to the use of composite fibers are discussed. The latter include challenges for poling and electrically wiring the fibers to collect charges under operation, or to apply electrical fields. The electromechanical properties of these fibers processed by different manufacturing techniques are compared. Recent studies of structures used to integrate such fibers in textiles and composites with conventional techniques and their potential applications are discussed.