This paper summarizes new aerial robotic manipulation technologies and methods, required for outdoor industrial inspection and maintenance, developed in the AEROARMS project. It presents the first aerial robotic manipulators with dual arms and multi-directional thrusters. It deals with the control systems, including the control of the interaction forces and the compliance, the teleoperation, which uses passivity to tackle the trade-off between stability and performance, perception methods for localization, mapping and inspection, and planning methods, including a new control-aware approach for aerial manipulation. Finally, it describes a novel industrial platform with multi-directional thrusters and a new arm design to increase the robustness in industrial contact inspections. The lessons learned in the application to outdoor aerial manipulation for inspection and maintenance are pointed out.