The study of toric arrangements is rooted in the literature in both its topological and its combinatorial aspects. Recent work of De Concini, Procesi and Vergne provided a fresh impulse towards a comprehensive study of this subject, viewed as a generalization of the successful theory of hyperplane arrangements in vector spaces. Out of this impulse grew new results, techniques and problems which I will try to survey with an eye towards setting up a general combinatorial-topological framework - thus pursuing a classical line of research which aims at the combinatorial and topological study of more general types of arrangements of submanifolds.
Some of the results I will present have been obtained in joint works with Karim Adiprasito, Filippo Callegaro, Giacomo d'Antonio or Sonja Riedel.