This study presents a literature review on the concept of power system flexibility in terms of its definition, indices, algorithms, implementation, economic impacts, operational impacts, and security. Although there are tremendous reviews on this subject in the literature, each paper discusses specific aspects of flexibility. Moreover, the literature is devoid of a comprehensive review of the latest improvements in terms of implementation, operation, and economics, which are addressed by the collections presented in this study. This paper, therefore, surveys some improvements that have been made in recent decades. Furthermore, we highlight the impact of the high penetration of renewable energy and energy storage systems towards enhancing the improvement of power system flexibility.