Federated Learning (FL) in smart healthcare systems is an innovative approach to distributed analysis of medical data while preserving confidentiality. By enabling collaborative learning without compromising patient privacy, FL offers a promising solution to the growing need for more efficient and secure medical applications. Researchers have been investigating various FL approaches to address the challenges in smart healthcare, with a focus on improving data use while maintaining high privacy assurance levels. In this paper, an analysis of aggregation models and secure aggregation techniques in smart healthcare to ensure privacy is presented. Then, we provide a comprehensive review of recent advances and applications of FL in smart healthcare systems. We analyze several FL-based approaches proposed in the literature, highlighting their strengths, limitations and potential impact on healthcare systems performance. In addition, we propose a taxonomy to classify the existing FL-based approaches.