At proposed future hadron colliders and in the coming years at the LHC, top quarks will be produced at genuinely multi-TeV energies. Top-tagging at such high energies forces us to confront several new issues in terms of detector capabilities and jet physics. Here, we explore these issues in the context of some simple JHU/CMS-type declustering algorithms and the N-subjettiness jet-shape variable tau(32). We first highlight the complementarity between the two tagging approaches at particle level with respect to discriminating top-jets against gluons and quarks, using multivariate optimization scans. We then introduce a basic fast detector simulation, including electromagnetic calorimeter showering patterns determined from GEANT. We consider a number of tricks for processing the fast detector output back to an approximate particle-level picture. Re-optimizing the tagger parameters, we demonstrate that the inevitable losses in discrimination power at very high energies can typically be ameliorated. For example, percent-scale mistag rates might be maintained even in extreme cases where an entire top decay would sit inside of one hadronic calorimeter cell and tracking information is completely absent. We then study three novel physics effects that will come up in the multi-TeV energy regime: gluon radiation off of boosted top quarks, mistags originating from g -> t (t) over bar, and mistags originating from q -> (W/Z)(q) collinear electroweak splittings with subsequent hadronic decays. The first effect, while nominally a nuisance, can actually be harnessed to slightly improve discrimination against gluons. The second effect can lead to effective O(1) enhancements of gluon mistag rates for tight working points. And the third effect, while conceptually interesting, we show to be of highly subleading importance at all energies.