This paper presents a general description of local flexibility markets as a market-based management mechanism for aggregators. The high penetration of distributed energy resources introduces new flexibility services like prosumer or community self-balancing, congestion management and time-of-use optimization. This work is focused on the flexibility framework to enable multiple participants to compete for selling or buying flexibility. In this framework, the aggregator acts as a local market operator and supervises flexibility transactions of the local energy community. Local market participation is voluntary. Potential flexibility stakeholders are the distribution system operator, the balance responsible party and end-users themselves. Flexibility is sold by means of loads, generators, storage units and electric vehicles. Finally, this paper presents needed interactions between all local market stakeholders, the corresponding inputs and outputs of local market operation algorithms from participants and a case study to highlight the application of the local flexibility market in three scenarios. The local market framework could postpone grid upgrades, reduce energy costs and increase distribution grids’ hosting capacity.