Anomalies in education affect the personal careers of students and universities' retention rates. Understanding the laws behind educational anomalies promotes the development of individual students and improves the overall quality of education. However, the inaccessibility of educational data hinders the development of the field. Previous research in this field used questionnaires, which are time- and cost-consuming and hardly applicable to large-scale student cohorts. With the popularity of educational management systems and the rise of online education during the prevalence of COVID-19, a large amount of educational data is available online and offline, providing an unprecedented opportunity to explore educational anomalies from a data-driven perspective. As an emerging field, educational anomaly analytics rapidly attracts scholars from a variety of fields, including education, psychology, sociology, and computer science. This paper intends to provide a comprehensive review of data-driven analytics of educational anomalies from a methodological standpoint. We focus on the following five types of research that received the most attention: course failure prediction, dropout prediction, mental health problems detection, prediction of difficulty in graduation, and prediction of difficulty in employment. Then, we discuss the challenges of current related research. This study aims to provide references for educational policymaking while promoting the development of educational anomaly analytics as a growing field.