The prediction of Intensive Care Unit (ICU) readmission has become a crucial area of research due to the increasing demand for ICU resources and the need to provide timely interventions to critically ill patients. In recent years, several studies have explored the use of statistical, machine learning (ML), and deep learning (DL) models to predict ICU readmission. This review paper presents an extensive overview of these studies and discusses the challenges associated with ICU readmission prediction. We categorize the studies based on the type of model used and evaluate their strengths and limitations. We also discuss the performance metrics used to evaluate the models and their potential clinical applications. In addition, this review explores current methodologies, data usage, and recent advances in interpretability and explainable AI for medical applications, offering insights to guide future research and development in this field. Finally, we identify gaps in the current literature and provide recommendations for future research. Recent advances like ML and DL have moderately improved the prediction of the risk of ICU readmission. However, more progress is needed to reach the precision required to build computerized decision support tools.