Recent advancements in computing systems and wireless communications have made healthcare systems more efficient than before. Modern healthcare devices can monitor and manage different health conditions of patients automatically without any manual intervention from medical professionals. Additionally, the use of implantable medical devices, body area networks, and Internet of Things technologies in healthcare systems improve the overall patient monitoring and treatment process. However, these systems are complex in software and hardware, and optimizing between security, privacy, and treatment is crucial for healthcare systems because any security or privacy violation can lead to severe effects on patients’ treatments and overall health conditions. Indeed, the healthcare domain is increasingly facing security challenges and threats due to numerous design flaws and the lack of proper security measures in healthcare devices and applications. In this article, we explore various security and privacy threats to healthcare systems and discuss the consequences of these threats. We present a detailed survey of different potential attacks and discuss their impacts. Furthermore, we review the existing security measures proposed for healthcare systems and discuss their limitations. Finally, we conclude the article with future research directions toward securing healthcare systems against common vulnerabilities.