Scientific review on the Complex Eikonal, and research perspectives for the Ionospheric Ray-tracing and Absorption he present paper conducts a scientific review on the complex eikonal, extrapolating the research perspectives on the ionospheric ray-tracing and absorption. As regards the scientific review, the eikonal equation is expressed, and some complex-valued solutions are defined corresponding to complex rays and caustics. Moreover, the geometrical optics is compared to the beam tracing method, introducing the limit of the quasi-isotropic and paraxial complex optics approximations. Finally, the quasi-optical beam tracing is defined as the complex eikonal method applied to ray-tracing, discussing the beam propagation in a cold magnetized plasma. As regards the research perspectives, this...