The adaptive response to hypoxia, low oxygen tension, involves inhibition of energy-intensive cellular processes including protein translation. This effect is mediated in part through a decrease in the kinase activity of mammalian target of rapamycin complex 1 (mTORC1), a master regulator of protein translation. The principle mechanism for hypoxia-induced mTORC1 inhibition, however, was not elucidated until recently. Our work has demonstrated that the stress-induced protein REDD1 is essential for hypoxia regulation of mTORC1 activity and has further defined the molecular mechanism whereby REDD1 represses mTORC1 activity under hypoxic stress. Using our studies with REDD1 as an example, we describe in detail biochemical approaches to assess mTORC1 activity in the hypoxic response. Here, we provide methodologies to monitor signaling components both downstream and upstream of the hypoxia-induced mTORC1 inhibitory pathway. These methodologies will serve as valuable tools for researchers seeking to understand mTORC1 dysregulation in the context of hypoxic stress.