The cold start phase of diesel engines is the primary stage for NO_x emissions, posing a severe threat to environmental pollution and human health. To address this issue, passive NO_x adsorbers (PNA) offer an effective solution for achieving ultra-low NO_x emissions in diesel exhaustafter treatment. This review summarizes recent advancements in PNA, exploring material design, invesigation of mechanisms, and performance evaluation. The evaluation focuses on the characteristics of two prominent PNA materials: transition metal oxides and zeolites, including their adsorption/desorption performance, oxidizing activity, and stability. Two NO_x adsorption-desorption mechanismsare proposed. The first mechanism involves the storage of NO_x as nitrite/nitrate, which decomposes with increasing temperature. The second mechanism involves the storage and release of NO_x as ionic complexes. Furthermore, the effects of exhaust components, such as H_2O, CO, and HC, on the NO_x adsorption-desorption behavior of PNA materials are discussed. The impact of hydrothermal aging and chemical poisoning (phosphorus and sulfur) on PNA materials is also examined. Finally, we outline the main challenges for future research on PNA materials.