As one of the efforts to overcome the problem of climate change, increasing the share of renewable energy (RE) in the national energy mix has become intensive in many countries, especially after the ratification of the Paris Agreement in 2015. Although this effort can effectively reduce carbon emissions, challenges to the security of power systems with increasing RE penetration are also emerging. This paper aims to provide an overview of several security issues on power systems, along with challenges arising from the impact of inertial reduction, RE fluctuations, RE prediction errors, and fault response, addressed to researchers as a reference for further studies. Case studies of security issues experienced by several system operators (SOs) when RE penetration is high in their electrical grids are discussed as a lesson for modern power systems operations. Moreover, measures to prevent and overcome these problems are proposed, including the need for changes and development in security assessment, protection and control schemes, and more relevant services for facing system security challenges in the future.