A thorough literature review is conducted that pertains to low-salinity-based enhanced oil recovery (EOR). This is meant to be a comprehensive review of all the refereed published papers, conference papers, master’s theses and other reports in this area. The review is specifically focused on establishing various relations/characteristics or “screening criteria” such as: (1) classification/grouping of clays that have shown or are amenable to low-salinity benefits; (2) clay types vs. range of residual oil saturations; (3) API gravity and down hole oil viscosity range that is amenable for low salinity; (4) salinity range for EOR benefits; (5) pore sizes, porosity, absolute permeability and wettability range for low-salinity EOR; (6) continuous low-salinity injection vs. slug-wise injection; (7) grouping of possible low-salinity mechanisms; (8) contradictions or similarities between laboratory experiments and field evidence; and (9) compositional variations in tested low-salinity waters. A proposed screening criterion for low-salinity waterflooding is introduced. It can be concluded that either one or more of these mechanisms, or a combination thereof, may be the case-specific mechanism, i.e., depending on the particular oil–brine–rock (OBR) system rather than something that is “universal” or universally applicable. Therefore, every OBR system that is unique or specific ought to be individually investigated to determine the benefits (if any) of low-salinity water injection; however, the proposed screening criteria may help in narrowing down some of the dominant responsible mechanisms. Although this review primarily focuses on sandstones, given the prominence of carbonates containing ~60% of the world’s oil reserves, a summary of possible mechanisms and screening criteria, pertaining to low-salinity waterflooding, for carbonates is also included. Finally, the enhancement of polymer flooding by using low-salinity water as a makeup water to further decrease the residual oil saturation is also discussed.