A supermassive black hole ejected from the center of a galaxy by gravitational-wave recoil carries a retinue of bound stars—a "hypercompact stellar system" (HCSS). The numbers and properties of HCSSs contain information about the merger histories of galaxies, the late evolution of binary black holes, and the distribution of gravitational-wave kicks. We relate the structural properties (size, mass, density profile) of HCSSs to the properties of their host galaxies and to the size of the kick in two regimes: collisional (M _BH 10⁷ M _☉), i.e., short nuclear relaxation times, and collisionless (M _BH 10⁷ M _☉), i.e., long nuclear relaxation times. HCSSs are expected to be similar in size and luminosity to globular clusters, but in extreme cases (large galaxies, kicks just above escape velocity) their stellar mass can approach that of ultracompact dwarf galaxies. However, they differ from all other classes of compact stellar system in having very high internal velocities. We show that the kick velocity is encoded in the velocity dispersion of the bound stars. Given a large enough sample of HCSSs, the distribution of gravitational-wave kicks can therefore be empirically determined. We combine a hierarchical merger algorithm with stellar population models to compute the rate of production of HCSSs over time and the probability of observing HCSSs in the local universe as a function of their apparent magnitude, color, size, and velocity dispersion, under two different assumptions about the star formation history prior to the kick. We predict that ~10² HCSSs should be detectable within 2 Mpc of the center of the Virgo cluster, and that many of these should be bright enough that their kick velocities (i.e., velocity dispersions) could be measured with reasonable exposure times. We discuss other strategies for detecting HCSSs and speculate on some exotic manifestations.