Efficient charge transport is often needed in electronic devices. For instance, the efficiency of solar cells is degraded when charges cannot leave the device fast enough. In transistors, carrier mobility is directly linked to the transit time across the channel and therefore to switching speed. Charge transport in organic semiconductors is limited by “trapping” where this word is used in a broad sense. In crystalline materials, the origin of traps remains unknown. Using high-quality single crystals and careful modeling of the space-charge-limited currents, I will show that the effect of intentional traps can be detected, which provides insights into the nature of intrinsic transport-limiting traps. In polycrystalline films on the other hand, the relationship between grain-boundaries and traps is unclear. In conjugated polymers, traps can be due to structural disorder within aggregates. The trap density in P3HT for instance is found to correlate to theoretical calculations. A different category of traps is due to morphological defects, such as chain bends or chain ends where charges can remain stuck. Understanding the different roles of these trapping mechanisms in limiting transport may provide useful insights to design higher efficiency organic semiconductors.