This article presents a comprehensive review of the state-of-the-art applications and methodologies related to the use of unmanned aerial vehicles (UAVs) in the healthcare sector, with a particular focus on path planning. UAVs have gained remarkable attention in healthcare during the outbreak of COVID-19, and this study explores their potential as a viable option for medical transportation. The survey categorizes existing studies by mission type, challenges addressed, and performance metrics to provide a clearer picture of the path planning problems and potential directions for future research. It highlights the importance of addressing the path planning problem and the challenges that UAVs may face during their missions, including the UAV delivery range limitation, and discusses recent solutions in this field. The study concludes by encouraging researchers to conduct their studies in a realistic environment to reveal UAVs' real potential, usability, and feasibility in the healthcare domain.