Superlattices are artificial periodic nanostructures which can control the flow of electrons. Their operation typically relies on the periodic modulation of the electric potential in the direction of electron wave propagation. Here we demonstrate transparent graphene superlattices which can manipulate infrared photons utilizing the collective oscillations of carriers, i.e., plasmons of the ensemble of multiple graphene layers. The superlattice is formed by depositing alternating wafer-scale graphene sheets and thin insulating layers, followed by patterning them all together into 3-dimensional photonic-crystal-like structures. We demonstrate experimentally that the collective oscillation of Dirac fermions in such graphene superlattices is unambiguously nonclassical: compared to doping single layer graphene, distributing carriers into multiple graphene layers strongly enhances the plasmonic resonance frequency and magnitude, which is fundamentally different from that in a conventional semiconductor superlattice. This property allows us to construct widely tunable far-infrared notch filters with 8.2 dB rejection ratio and terahertz linear polarizers with 9.5 dB extinction ratio, using a superlattice with merely five graphene atomic layers. Moreover, an unpatterned superlattice shields up to 97.5% of the electromagnetic radiations below 1.2 terahertz. This demonstration also opens an avenue for the realization of other transparent mid- and far-infrared photonic devices such as detectors, modulators, and 3-dimensional meta-material systems.