Sleep disorders are a common health condition that can affect numerous aspects of life. Obstructive sleep apnea is one of the most common disorders and is characterized by a reduction or cessation of airflow during sleep. In many countries, this disorder is usually diagnosed in sleep laboratories, by polysomnography, which is an expensive procedure involving much effort for the patient. Multiple systems have been proposed to address this situation, including performing the examination and analysis in the patient's home, using sensors to detect physiological signals that are automatically analyzed by algorithms. However, the precision of these devices is usually not enough to provide clinical diagnosis. Therefore, the objective of this review is to analyze already existing algorithms that have not been implemented on hardware but have had their performance verified by at least one experiment that aims to detect obstructive sleep apnea to predict trends. The performance of different algorithms and methods for apnea detection through the use of different sensors (pulse oximetry, electrocardiogram, respiration, sound, and combined approaches) has been evaluated. 84 original research articles published from 2003 to 2017 with the potential to be promising diagnostic tools have been selected to cover multiple solutions. This paper could provide valuable information for those researchers who want to carry out a hardware implementation of potential signal processing algorithms.