A hydrocarbon and NOx trap and related apparatus and methods for reducing cold-start NOx emissions from an engine are provided. In one embodiment a trap includes a first, topmost layer, exposed to an exhaust gas flow path of exhaust gases from an engine, the first layer comprising a zeolite, a second layer, substantially covered by the top most layer, the second layer comprising a NOx adsorbing material and a monolithic substrate, directly supporting the second layer and indirectly supporting the first layer, the substrate providing a substantially rigid structure of the trap.