The aim of this chapter is twofold. First, we introduce the information loss problem; second, we provide a critical assessment by thoroughly inspecting the assumptions underlying its formulations. In particular, we argue that if we work in the regime of validity of semiclassical gravity and do not add additional assumptions that are not necessary for the Hawking calculation, the answer to the question in the title is NO. In other words, the black hole evaporation is certainly unitary as predicted by quantum field theory in curved spacetime. However, if additional assumptions are added, such as a universal area bound on the entropy, contradictions may arise even in regimes where we would expect the semiclassical approximation to be valid. We show that a contradiction indeed arises, but not between the laws of semiclassical general relativity and quantum mechanics, but rather between the former and the additional (holographic) requirement of the area limit, according to which an exterior observer describes a black hole as a quantum system whose entropy is bounded by its area.