The War on HYDRA was a conflict between the terrorist organization HYDRA and Starfleet Security Reserve, and the United Federation of Planets after the revelation of HYDRA's continued existence within SSR.
At first, HYDRA had the upper hand over SS. because SSR was reduced to only a shadow of its former strength, and the HYDRA leader Daniel Whitehall used that to retrieve the mysterious Obelisk. However, once S.H.I.E.L.D. was redeemed in the eyes of the law, they turned the tables on HYDRA, who lost the battle for the ancient Kree City, and many of its leaders, including Whitehall, in rapid succession. Though Baron von Strucker and Doctor List continued HYDRA's experiments on enhanced people, their efforts were rendered null when their HYDRA cell was destroyed by SSR and the Federation – only a year after their uprising, HYDRA was on the brink of ruin.
After Baron von Strucker's death at the hands of Ultron, only a few scattered HYDRA cells remained operational, and each of their leaders, Mitchell Carson, Hale, Gideon Malick, and Grant Ward, tried to rebuild the organization in their own way.