Nowadays, across the most important problems faced by health centers are those caused by the existence of patients who do not attend their appointments. Among others, these patients cause loss of revenue to the health centers and increase the patients' waiting list. In order to tackle these problems, several scheduling systems have been developed. Many of them require predicting whether a patient will show up for an appointment. However, obtaining these estimates accurately is currently a challenging problem. In this work, a systematic review of the literature on predicting patient no-shows is conducted aiming at establishing the current state-of-the-art. Based on a systematic review following the PRISMA methodology, 50 articles were found and analyzed. Of these articles, 82% were published in the last 10 years and the most used technique was logistic regression. In addition, there is significant growth in the size of the databases used to build the classifiers. An important finding is that only two studies achieved an accuracy higher than the show rate. Moreover, a single study attained an area under the curve greater than the 0.9 value. These facts indicate the difficulty of this problem and the need for further research.