The chapter provides an overview of the basic modeling and the intrinsic properties of aerial platforms with multi-directional total thrust ability. When also fully-actuated, such platforms can modify the total wrench in body frame in any direction, thus allowing the control of position and orientation independently. There- fore, they are best suited for dexterous tasks, physical interaction, and for carrying aerial manipulators, because they do not suffer from the underactuation of standard collinear multirotors. The chapter includes a rigorous classification, a discussion on the possible input coupling, and on the capabilities and pitfalls of inverse-dynamics control approach for such platforms.