Spin-orbit interactions in bulk heavy metals, or at Rashba interfaces (or Topological Insulators interfaces) are at the origin of intriguing physical phenomena like spin Hall effects (SHE) and Inverse Spin-Hall effects [1] as well as Inverse Edelstein Effects (IEE) [2] leading to spin-to-charge conversion near interfaces of and interface states. These novel spinorbitronics effects, investigated here, are presently of a large interest in order to develop THz emitter devices like recently demonstrated in international spintronics laboratories worldwide [3-5]. On the ground of a very recent literature, I will first present our main latest experimental investigations, refined analyses and models related to the SHE occurring in 3d transition ferromagnets/Pt heavy metals [6] and 3d/Au:W bilayers combining spin-pumping spin-current injection and IEE [7]. In a second part, I will discuss the spin-to-charge conversion at the interface of LaAlO3/SrTiO3 Oxide Rashba electron gas [8] and Fe/Ge(111) Rashba systems [9] mediated by both the linear and cubic Rashba (111 direction) interactions and scaled by the IEE length. In these experiments, the spin-pumping mechanism in the ferromagnetic resonance regime (FMR) allows spin-current injection along the perpendicular direction whereas the necessary spin-orbit field allows its efficient conversion to a lateral charge current. We will discuss the different possible mechanism leading to such spin-to-charge conversion [10].