We systematically investigate the spatial/temporal photocurrent in photodetectors and electronic transport in transistors/Hall-bar devices based on monolayer MoS2 grown by chemical vapor deposition (CVD). We found that the maximum photocurrent occurs when the laser spot is close to the metal/MoS2 contact and is tunable by the applied drain voltage, which can be explained by the modulation of the local electric field at the Schottky barrier, consistent with predictions from our quantum transport simulation. We observed that the maximum photocurrent at drain contact is much larger than the one at the source contact, and the DC currents show rectifying behavior. These phenomena can be explained by the different Schottky barrier heights at the two contacts. By measuring Hall-bar structure at various temperatures from 100 K to 400 K, we extracted the barrier heights at the source and drain contacts, separately. We found that the barrier height at drain contact is about 50 mV larger than the one at the source contact, consistent with the photocurrent and DC current observations. We measured the photocurrent at various powers, and a photoresponsivity of 3.07 mA/W was extracted at low powers. When the power increases above 20 μW, the photocurrent starts to saturate. Temporal response of the photocurrent is also dependent on the laser power. At high laser powers, photocurrent overshoot was observed. The photocurrent saturation at high powers and the overshoot in temporal photocurrent are likely due to the same mechanism: an accumulation of electrons in the channel, flattening out the band structure, since the laser spot is located near the drain contact in these measurements. These studies of photocurrents and electronic transport in CVD MoS2 highlight the importance of the contacts in the electronic/optoelectronic devices and reveal the physical mechanism of the photocurrent/electronic transport in these devices.