To identify the trends in new flexibility markets, a set of market and aggregator platforms were selected and compared. The analyzed initiatives are relevant to consider alternative designs for European electricity markets. This review proposes a common methodology for analyzing these market models by comparing their description, market structure, market timing, and implementation. Furthermore, a range of policy implications and future research directions towards implementing these markets are presented. The results provide compelling evidence that the new market models represent a promising business with technical and economic justification, as they incentivize the uptake of flexibility from distributed resources by providing services to Distribution System Operators (DSOs) in coordination with Transmission System Operators (TSOs). Moreover, the interactions between these new market platforms and existing markets are of particular interest, and the contributions from aggregator platforms are also relevant to enhance the political vision of empowering the customers through their active participation in markets.