Graphene has various potential applications owing to its unique electronic, optical, mechanical and chemical properties, which are primarily based on its two-dimensional nature. Graphene-based vertical devices can extend the investigations and potential applications range to three dimensions, while interfacial properties are crucial for the function and performance of such graphene vertical devices. Here we report a general method to construct graphene vertical devices with controllable functions via choosing different interfaces between graphene and other materials. Two types of vertically conducting devices are demonstrated: graphene stacks sandwiched between two Au micro-strips, and between two Co layers. The Au|graphene|Au junctions exhibit large magnetoresistance with ratios up to 400% at room temperature, which have potential applications in magnetic field sensors. The Co|graphene|Co junctions display a robust spin valve effect at room temperature. The layer-by-layer assembly of graphene offers a new route for graphene vertical structures.