The increasing instabilities in power transmission and distribution necessitate power grid operators to enhance their utilization of communication infrastructure for the purpose of monitoring and controlling the grid. However, this heightened communication activity also creates a larger vulnerability for malicious individuals. Incidents of cyber-attacks on power grids have already caused significant, temporary blackouts in recent times. This study examines the communication infrastructure of power grids and identifies the fundamental cybersecurity challenges that arise as a result. Subsequently, a wide range of potential attack vectors and scenarios that pose a threat to power grid security are identified. To address these challenges, this paper proposes the adoption of a defense-in-depth strategy that includes measures for device and application security, network security, physical security, as well as policies, procedures, and awareness. Within each of these categories, this paper present a comprehensive collection of cutting-edge approaches and highlight additional opportunities to enhance cybersecurity in interconnected power grids.