New developments in the nascent field of organic spintronics are discussed. Two classes of phenomena can be discerned. In hybrid organic spin valves (OSVs), an organic semiconducting film is sandwiched between two ferromagnetic (FM) thin films, aiming at magnetoresistive effects as a function of the relative alignment of the respective magnetization directions. Alternatively, organic magnetoresistance (OMAR) is achieved without any FM components, and is an intrinsic property of the organic semiconductor material. Some of the exciting characteristics of OMAR, in both electrical conductance and photoconductance, are presented. A systematic, combined experimental-theoretical study of sign changes between positive and negative magnetoresistance is shown to provide important insight about the underlying mechanisms of OMAR. A simple explanation of experimental observations is obtained by combining a spin-blocking mechanism, an essential ingredient in the recently proposed bipolaron model, with specific features of the device physics of space charge limited current devices in the bipolar regime. Finally, we discuss possible links between the physics relevant for OMAR and that for OSVs. More specifically, weak hyperfine fields from the hydrogen atoms in organic materials are thought to be crucial for a proper understanding of both types of phenomena.