The explosive growth of biomedical literature and clinical data is increasing the difficulty for healthcareprofessionals to continuously access new information. This survey summarizes the state-of-the-art studies inbiomedical text summarization (extractive, abstractive, and hybrid) and their implementations. In this regard, thesurvey delves into the influence of deep learning and natural language processing (NLP) methods on enhancingsummarization capabilities while simultaneously highlighting ongoing challenges related to domain-specific jargon,truthfulness, and explainability. The paper further describes some evaluation metrics and datasets specific tobiomedical problems that are important for both training and evaluating summarization models. Finally, wehighlight three of these considerations that we believe are worth pursuing in future work toward designing moreeffective and grounded summarization systems. Biomedical text summarization, which extracts useful informationfrom vast quantities of data, might help render scientific knowledge more reachable, assist clinical decision-makingand policy, and potentially push research forward