We study marginally trapped surfaces, that is, closed embedded spacelike 2-surfaces of a 4-dimensional spacetime whose mean curvature vector is everywhere timelike. These surfaces were introduced by R. Penrose to study singularities of spacetimes, but appeared much earlier in Blaschke’s work on conformal and Laguerre geometry. They play an extremely important role in general relativity, where they are of central importance in the study of black holes. Mathematically, marginally trapped surfaces are regarded as spacetime analogues of minimal surfaces in Riemannian geometry. We argue via fundamental examples that a very large class of marginally trapped surfaces arise naturally from a light-like co-contact structure, exactly in the same way as Legendrian fronts arise from a contact one by projection of a Legendrian submanifold to the base of a Legendrian fibration, and that there is an adjunction relationship between both notions. We especially focus on marginally trapped hedgehogs and their relationships with Laguerre geometry and Brunn-Minkowski theory.