Cellular needs are fulfilled by the combined activity of functional proteins. Consequently, cells are equipped with a complex proteostatic network that controls protein production in response to cellular requisites. Thereby, protein synthesis is induced or attenuated depending on the particular cellular conditions. One of the mechanisms to control protein synthesis is the phosphorylation of eIF2, which triggers the so-called Integrated Stress Response (ISR). Kinases that sense stresses induce the phosphorylation of eIF2, which, on the one hand, attenuates global rates of protein synthesis and, on the other hand, activates the expression of specific proteins that help to alleviate the stress. One of the proteins preferentially expressed during the ISR is PPP1R15A, a regulatory subunit of Protein Phosphatase 1 (PP1). The PP1/PPP1R15A holophosphatase dephosphorylates eIF2 and terminates the ISR once the stresses are resolved. Hence, eIF2 kinases and phosphatases work together to control levels of phosphorylated eIF2. Maintaining the right balance between the activity of these kinases and phosphatases is important, as is seen by the correlation between their perturbance and the appearance of certain cellular malfunctions or diseases. However, affecting this balance has been also suggested to have beneficial effects. For example, genetic interference with the PPP1R15A regulatory subunit is proposed to confer protection to mice and cells under ER-stress conditions. This observation led to the search for compounds with the ability to modulate the ISR, in particular, by acting on the eIF2 phosphatases. Three compounds (Salubrinal, Guanabenz and Sephin1) have been proposed as eIF2 phosphatase inhibitors with potential use as therapeutic tools in protein misfolding diseases. However, their precise mechanism of action and their direct effect on the enzyme remains an open question. This thesis focuses on the in vitro reconstitution of the eIF2 phosphatase, which served as a platform for characterizing the enzyme (in terms of its structure, activity and assembly) and for studying the proposed inhibitors. This report details key structural features of the PPP1R15/PP1 holophosphatase, the discovery of a cellular cofactor of the enzyme and the conclusions obtained after analysing the effect of its proposed inhibitors. It also includes the development of several in vitro assays, which could potentially be used to screen libraries of compounds in search for modulators of the enzyme.