In this survey talk I will present some results, obtained in collaboration with Michael Ruzhansky (Ghent/QMUL), Christian Jäh (Göttingen) and Bolys Sabitbek (QMUL), on hyperbolic equations and systems with multiplicities. In particular, I will discuss the conditions needed on the lower order terms (Levi conditions) to prove the well-posedness of the corresponding Cauchy problem.