Massive proliferation of Variable Energy Resources (VERs) in modern power systems has posed a variety of challenges to the reliable operation of the power grid and has, at times, jeopardized the system flexibility. Flexibility is the system's ability to respond to and cope with the imbalances between supply and demand while managing the uncertainty and variability of VERs and maintaining the power system's security and reliability within the acceptable margins. Leveraging the system's available resources and capabilities, the system operators must take strategic actions to mitigate the impacts of VERs on the grid flexibility at a reasonable cost. The concept of flexibility is somewhat novel, which calls for profound studies and analyses to address different aspects of flexibility, but not limited to definition and characterization of standard metrics and indices to measure the power grid flexibility, flexibility-centred operation and planning models for the power grid, etc. This paper provides a comprehensive review of the state-of-the-art research on power system flexibility, including existing definitions and quantification measures, flexible resources, and flexibility products and services in electricity markets.