Electric power systems are moving toward more decentralized models, where energy generation is performed by small and distributed power plants, often from renewables. With the gradual phase out from fossil fuels, however, Distribution Energy Resources (DERs) are expected to take over in the provision of all regulation services required to operate the grid. To this purpose, the opening of national Ancillary Service Markets (ASMs) to DERs is considered an essential passage. In order to allow this transition to happen, current opportunities and barriers to market participation of DERs must be clearly identified. In this work, a comprehensive review is provided of the state-of-the-art of research on DER integration into ASMs. The topic at hand is analyzed from different perspectives. First, the current situation and main trends regarding the reformation processes of national ASMs are analyzed to get a clear picture of the evolutions expected and adjustment required in the future, according to the scientific community. Then, the focus is moved to the strategies to be adopted by aggregators for the effective control and coordination of DERs, exploring the challenges posed by the uncertainties affecting the problem. Coordination schemes between transmission and distribution system operators, and the implications on the grid infrastructure operation and planning, are also investigated. Finally, the review deepens the control capabilities required for DER technologies to perform the needed control actions.