As healthcare technologies advance, their increasing interconnectivity and integration into more extensive IT networks and systems offer numerous advantages, such as real-time remote monitoring, early prevention and cost reduction. However, this heightened interconnectedness also presents significant challenges, with cyberattacks targeting medical devices and hospital networks emerging as prominent issues. Understandably, the cybersecurity of connected medical devices has gained paramount importance and urgency. This paper outlines the principal cybersecurity challenges confronting the healthcare sector and introduces insights from the EU-funded CYLCOMED project, which aims to provide the latest technological solutions to address these challenges. Mainly, the paper seeks to identify the primary challenges encountered by the healthcare sector concerning cyber threats. Subsequently, it outlines the high-level architecture of the EU-funded CYLCOMED project (Cyber securitY tooLbox for COnnected MEdical Devices) and its principal objectives, which aim to enhance the cybersecurity of connected, in vitro diagnostic, and software as medical devices (CMDs, IVDs, SaMD). Lastly, it provides a brief overview of the applicable EU legal framework governing the cybersecurity of medical devices.