The charge transport characteristics of organic semiconductors are one of the key attributes that impacts the performance of organic electronic and optoelectronic devices in which they are utilized. For improved performance in organic photovoltaic cells, light-emitting diodes, and field-effect transistors (FETs), efficient transport of the charge carriers within the organic semiconductor is especially critical. Characterization of charge transport in these organic semiconductors is important both from scientific and technological perspectives. In this review, we shall mainly discuss the techniques for measuring the charge carrier mobility and not the theoretical underpinnings of the mechanism of charge transport. Mobility measurements in organic semiconductors and particularly in conjugated polymers, using space-charge-limited current, time of flight, carrier extraction by linearly increasing voltage, double injection, FETs, and impedance spectroscopy are discussed. The relative merits, as well as limitations for each of these techniques are reviewed.