The modern study of unitary representations of reductive groups over local fields has been greatly influenced by Arthur's conjectures on the parametrisation of the local factors of automorphic forms in the discrete spectrum. For reductive groups over real or p-adic fields, Arthur's local conjectures admit a precise formulation in the work of Adams, Barbasch, and Vogan, via the microlocal analysis of the geometric parameter space for the admissible dual of the group. In the case of p-adic groups, the geometric parameter space is given by the complex geometric setting of Kazhdan and Lusztig. An important particular case, where everything can be made precise, is the category of unipotent (in the sense of Lusztig) representations of a reductive p-adic group; these are the representations for which the Langlands parameters are unramified, in the sense of being trivial on the inertia subgroup of the Weil group. Once we fix an"infinitesimal character" for the representations, the geometry comes from the action of a complex reductive group on a complex vector space with finitely many orbits; for the Adams-Barbasch-Vogan picture, we are interested in the resulting microlocal packets and the corresponding packets of irreducible representations of the p-adic group. In the talk, I will explain the parametrisations and above constructions, give examples, and concentrate on the integral infinitesimal characters, where some surprisingly strong general conjectures about unitarisability can be formulated.