Cannabis is commonly used, and use may be increasing in the setting of increasing legalization and social acceptance. The scope of the effects of cannabis products, including varieties with higher or lower levels of Δ9-tetrahydrocannabinol (THC) or cannabidiol (CBD), on domains related to addictive behavior deserves attention, particularly as legalization continues. Cannabis use may impact neural underpinnings of cognitive functions linked to propensities to engage in addictive behaviors. Here we consider these neurocognitive processes within the framework of the dual-process model of addictions. In this mini-review, we describe data on the relationships between two main constituents of cannabis (THC and CBD) and neural correlates of reward processing, inhibitory control and working memory.