Lead halide perovskites (LHPs) containing organic parts are emerging optoelectronic materials with a wide range of applications thanks to their high optical absorption, carrier mobility, and easy preparation methods. They possess spin-dependent properties, such as strong spin–orbit coupling (SOC), and are promising for spintronics. The Rashba effect in LHPs can be manipulated by a magnetic field and a polarized light field. Considering the surfaces and interfaces of LHPs, light polarization-dependent optoelectronics of LHPs has attracted attention, especially in terms of spin-dependent photocurrents (SDPs). Currently, there are intense efforts being made in the identification and separation of SDPs and spin-to-charge interconversion in LHP. Here, we provide a comprehensive review of second-order nonlinear photocurrents in LHP in regard to spintronics. First, a detailed background on Rashba SOC and its related effects (including the inverse Rashba–Edelstein effect) is given. Subsequently, nonlinear photo-induced effects leading to SDPs are presented. Then, SDPs due to the photo-induced inverse spin Hall effect and the circular photogalvanic effect, together with photocurrent due to the photon drag effect, are compared. This is followed by the main focus of nonlinear photocurrents in LHPs containing organic parts, starting from fundamentals related to spin-dependent optoelectronics. Finally, we conclude with a brief summary and future prospects.