In the study of hyperbolic 3-manifolds cusps play an important role. The geometry of a cusp is determined by a similarity structure on the boundary of the cusp. In the finite volume case, the boundary is a torus and the similarity structure is determined by a complex number with positive imaginary part. Properly-convex real-projective manifolds are a generalization of hyperbolic manifolds. In dimension 3 the moduli space of generalized cusps is a bundle over the space of similarity structures on the torus, with fiber a subspace of the space of (real) cubic differentials. Conjecturally a similar statement is true in all dimensions for cusps with compact boundary. There is a 9-dimensional cusp with fundamental group the integer Heisenberg group, and the classification of cusps with non-compact boundary is unknown. Joint: Sam Ballas, Arielle Leitner.