Biomedical informatics can be considered as a multidisciplinary research and educational field situated at the intersection of computational sciences (including computer science, data science, mathematics, and statistics), biology, and medicine. In recent years, there have been advances in the field of biomedical informatics. The current article highlights some interesting state-of-the-art research outcomes in these fields. These include research outcomes in areas like (i) computational biology and medicine, (ii) explainable artificial intelligence (XAI) in biomedical research and clinical practice, (iii) machine learning (including deep learning) methods and application for bioinformatics and healthcare, (iv) imaging informatics, as well as (v) medical statistics and data science. Moreover, the current article also discusses some existing challenges and potential future directions for these research areas to advance the fields of biomedical informatics.