Accurately predicting the time of occurrence of an event of interest is a critical problem in longitudinal data analysis. One of the main challenges in this context is the presence of instances whose event outcomes become unobservable after a certain time point or when some instances do not experience any event during the monitoring period. Such a phenomenon is called censoring which can be effectively handled using survival analysis techniques. Traditionally, statistical approaches have been widely developed in the literature to overcome this censoring issue. In addition, many machine learning algorithms are adapted to effectively handle survival data and tackle other challenging problems that arise in real-world data. In this survey, we provide a comprehensive and structured review of the representative statistical methods along with the machine learning techniques used in survival analysis and provide a detailed taxonomy of the existing methods. We also discuss several topics that are closely related to survival analysis and illustrate several successful applications in various real-world application domains. We hope that this paper will provide a more thorough understanding of the recent advances in survival analysis and offer some guidelines on applying these approaches to solve new problems that arise in applications with censored data. Machine Learning for Survival Analysis: A Survey