The physics potential of proton-nucleus collisions at the TeV scale

The LHC brings nuclear collisions to the TeV scale for the first time and the first data show the qualitative differences of this new regime. The corresponding phase-space available encompasses completely uncharted regions of QCD in which high-density or high-temperature domains can be identified. Proton-nucleus runs are essential for a complete interpretation of the data and for the study of new regimes dominated by large occupation numbers in the hadronic wave function. I comment here the physics opportunities for p+Pb runs at the LHC and d+Au runs at RHIC and the corresponding needs in view of the new Pb+Pb data from the LHC.