Tunable metasurfaces, whose functionality can be dynamically modified, open up the possibil-
ity of ultra-compact photonic components with reconfigurable applications. Here we consider a
graphene monolayer subject to a spatially periodic gate bias, which, thank to surface plasmons in
the graphene, acts as a tunable and extremely compact metasurface for terahertz radiation. After
characterizing its functionality, we show that it serves as the basic building block of an ultrathin
complete absorber. In this subwavelength-thickness device, transmission and reflection channels are
blocked and electromagnetic energy is completely absorbed by the metasurface building blocks. The
proposed structure can be used as a modulator, and its frequency of operation can be changed by
scaling its size or adjusting the doping level.