There exists an increasing interest in monitoring low concentrations of biochemical species, as they allow the early-stage detection of illnesses or the monitoring of the environment quality. Thus, both companies and research groups are focused on the development of accurate, fast and highly sensitive biosensors. Optical fiber sensors have been widely employed for these purposes because they provide several advantages for their use in point-of-care and real-time applications. In particular, this review is focused on optical fiber biosensors based on luminescence and absorption. Apart from the key parameters that determine the performance of a sensor (limit of detection, sensibility, cross-sensibility, etc.), other features are analyzed, such as the optical fiber dimensions, the sensing set ups and the fiber functionalization. The aim of this review is to have a comprehensive insight of the different aspects that must be taken into account when working with this kind of sensors.